Nuova ricerca

Olindo CORRADINI

Professore Associato
Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Fisica

Home | Curriculum(pdf) | Didattica |


Pubblicazioni

2023 - Avenues of Quantum Field Theory in Curved Spacetime, Genova, 14-16 Sep 2022 [Relazione in Atti di Convegno]
Carloni, S.; Cianci, R.; Corradini, O.; Flachi, A.; Vignolo, S.; Vitagliano, V.
abstract

2022 - An overview of physics teacher professional development activities organized within the Italian PLS-Physics plan over the past five years [Relazione in Atti di Convegno]
Michelini, M.; Malgieri, M.; Corradini, O.; De Angelis, I.; Bernarduzzi, L. F.; Giliberti, M.; Pagliara, S.; Pavesi, M.; Sabbarese, C.; Salamida, F.; Straulino, S.; Imme, J.
abstract

The Italian PLS-"Piano Lauree Scientifiche"project has among its objectives the improvement of school-university cooperation, with a special emphasis on in-service teacher professional development. In pursuit of such goal, growing resources and an increasing effort to strengthen the collaboration with schools have been employed in the past years. A working group within the physics section of the PLS project has developed a questionnaire to inquire about teacher formation activities organized during the past five years. After extensive revision and testing, the university network of PLS-Physics was asked to fill the questionnaire. The resulting data from 139 initiatives provides an interesting perspective on the kind of activities, organizational choices and educational priorities for teacher professional development within the PLS-physics project.

2022 - Dimensional regularization for the particle transition amplitude in curved space [Articolo su rivista]
Corradini, O.; Crispo, L.; Muratori, M.
abstract

We compute the perturbative short-time expansion for the transition amplitude of a particle in curved space time, by employing dimensional regularization (DR) to treat the divergences which occur in some Feynman diagrams. The present work generalizes known results where DR was applied to the computation of one-loop effective actions, which in the worldline approach are linked to particle path integrals on the circle, i.e. with periodic boundary conditions. The main motivation of the present work comes from revived interest in particle transition amplitudes in curved space-times, due to their use in the recently proposed worldline quantum field theory (in curved space-time).

2022 - Manifest colour-kinematics duality and double-copy in the string-based formalism [Articolo su rivista]
Ahmadiniaz, N.; Balli, F. M.; Corradini, O.; Lopez-Arcos, C.; Quintero Velez, A.; Schubert, C.
abstract

The relation for the gravity polarisation tensor as the tensor product of two gluon polarisation vectors has been well-known for a long time, but a version of this relation for multi-particle fields is presently still not known. Here we show that in order for this to happen we first have to ensure that the multi-particle polarisations satisfy colour-kinematics duality. In previous work it has been show that this arises naturally from the Bern-Kosower formalism for one-loop gluon amplitudes, and here we show that the tensor product for multi-particle fields arises naturally in the Bern-Dunbar-Shimada formalism for one-loop gravity amplitudes. This allows us to formulate a new prescription for double-copy gravity Berends-Giele currents, and to obtain both the colour-dressed Yang-Mills Berends-Giele currents in the Bern-Carrasco-Johansson gauge and the gravitational Berends-Giele currents explicitly. An attractive feature of our formalism is that it never becomes necessary to determine gauge transformation terms. Our double-copy prescription can also be applied to other cases, and to make this point we derive the double-copy perturbiners for α′-deformed gravity and the bi-adjoint scalar model.

2022 - Obtaining Fully Polarized Amplitudes in Gauge Invariant Form [Relazione in Atti di Convegno]
Ahmadiniaz, N.; Banda Guzman, V. M.; Bastianelli, F.; Corradini, O.; Edwards, J. P.; Schubert, C.
abstract

Abstract: We describe progress applying the Worldline Formalism of quantum field theory to the fermion propagator dressed by N-photons to study multi-linear Compton scattering processes, explaining how this approach—whose calculational advantages are well-known at multi-loop order—yields compact and manifestly gauge invariant scattering amplitudes.

2022 - Worldline master formulas for the dressed electron propagator. Part 2. On-shell amplitudes [Articolo su rivista]
Ahmadiniaz, N.; Guzman, V. M. B.; Bastianelli, F.; Corradini, O.; Edwards, J. P.; Schubert, C.
abstract

In the first part of this series, we employed the second-order formalism and the “symbol” map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open fermion-line calculations. Its main advantages are the avoidance of long products of Dirac matrices, and its ability to unify whole sets of Feynman diagrams related by permutation of photon legs along the fermion lines. We obtained a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the “N-photon kernel,” where this kernel appears also in “subleading” terms involving only N − 1 of the N photons. In this sequel, we focus on the application of the formalism to the calculation of on-shell amplitudes and cross sections. Universal formulas are obtained for the fully polarised matrix elements of the fermion propagator dressed with an arbitrary number of photons, as well as for the corresponding spin-averaged cross sections. A major simplification of the on-shell case is that the subleading terms drop out, but we also pinpoint other, less obvious simplifications. We use integration by parts to achieve manifest transversality of these amplitudes at the integrand level and exploit this property using the spinor helicity technique. We give a simple proof of the vanishing of the matrix element for “all +” photon helicities in the massless case, and find a novel relation between the scalar and spinor spin-averaged cross sections in the massive case. Testing the formalism on the standard linear Compton scattering process, we find that it reproduces the known results with remarkable efficiency. Further applications and generalisations are pointed out.

2021 - Bosons on a rotating ring with free boundary conditions [Articolo su rivista]
Corradini, O.; Flachi, A.; Marmorini, G.; Muratori, M.; Vitagliano, V.
abstract

We consider a system of interacting non-relativistic bosons confined to a onedimensional ring in the presence of a synthetic gauge field induced by a rotating barrier. Interactions are introduced as a constraint in field space, and the barrier is modeled by general boundary conditions.Within this setup, we compute the effective action and investigate the profile of the ground state and its sensitivity from rotational velocity and the properties of the barrier.

2021 - Dressed Dirac propagator from a locally supersymmetric N=1 spinning particle [Articolo su rivista]
Corradini, O.; Degli Esposti, G.
abstract

We study the Dirac propagator dressed by an arbitrary number N of photons by means of a worldline approach, which makes use of a supersymmetric N=1 spinning particle model on the line, coupled to an external Abelian vector field. We obtain a compact off-shell master formula for the tree level scattering amplitudes associated to the dressed Dirac propagator. In particular, unlike in other approaches, we express the particle fermionic degrees of freedom using a coherent state basis, and consider the gauging of the supersymmetry, which ultimately amounts to integrating over a worldline gravitino modulus, other than the usual worldline einbein modulus which corresponds to the Schwinger time integral. The path integral over the gravitino reproduces the numerator of the dressed Dirac propagator.

2021 - Quantum Darboux theorem [Articolo su rivista]
Corradini, O.; Latini, E.; Waldron, A.
abstract

The problem of computing quantum mechanical propagators can be recast as a computation of a Wilson line operator for parallel transport by a flat connection acting on a vector bundle of wave functions. In this picture, the base manifold is an odd-dimensional symplectic geometry, or quite generically a contact manifold that can be viewed as a "phase-spacetime,"while the fibers are Hilbert spaces. This approach enjoys a "quantum Darboux theorem"that parallels the Darboux theorem on contact manifolds which turns local classical dynamics into straight lines. We detail how the quantum Darboux theorem works for anharmonic quantum potentials. In particular, we develop a novel diagrammatic approach for computing the asymptotics of a gauge transformation that locally makes complicated quantum dynamics trivial.

2020 - A Monte Carlo approach to the worldline formalism in curved space [Articolo su rivista]
Corradini, O.; Muratori, M.
abstract

We present a numerical method to evaluate worldline (WL) path integrals defined on a curved Euclidean space, sampled with Monte Carlo (MC) techniques. In particular, we adopt an algorithm known as YLOOPS with a slight modification due to the introduction of a quadratic term which has the function of stabilizing and speeding up the convergence. Our method, as the perturbative counterparts, treats the non-trivial measure and deviation of the kinetic term from flat, as interaction terms. Moreover, the numerical discretization adopted in the present WLMC is realized with respect to the proper time of the associated bosonic point-particle, hence such procedure may be seen as an analogue of the time-slicing (TS) discretization already introduced to construct quantum path integrals in curved space. As a result, a TS counter-term is taken into account during the computation. The method is tested against existing analytic calculations of the heat kernel for a free bosonic point-particle in a D-dimensional maximally symmetric space.

2020 - Compton-like scattering of a scalar particle with N photons and one graviton [Articolo su rivista]
Ahmadiniaz, N.; Balli, F. M.; Corradini, O.; Davila, J. M.; Schubert, C.
abstract

Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number N of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude, where all the photons and the graviton are directly attached to the scalar line, then derive a “tree replacement” rule to construct the reducible parts of the amplitude which involve irreducible pure N-photon two-scalar amplitudes where one photon line emits the graviton. We test our construction by verifying the on-shell gauge and diffeomorphism Ward identities, at arbitrary N.

2020 - Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes [Articolo su rivista]
Ahmadiniaz, N.; Guzman, V. M. B.; Bastianelli, F.; Corradini, O.; Edwards, J. P.; Schubert, C.
abstract

In the first-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the “N -photon kernel,” where off-shell this kernel appears also in “subleading” terms involving only N − 1 of the N photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the N = 2 case for a recalculation of the one-loop fermion self energy, in D dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation by choosing an unusual momentum-dependent gauge parameter.

2019 - A worldline approach to colored particles [Relazione in Atti di Convegno]
Bastianelli, Fiorenzo; Bonezzi, Roberto; Corradini, Olindo; Latini, Emanuele; Ould-Lahoucine, Khaled Hassan
abstract

Relativistic particle actions are a useful tool to describe quantum field theory effective actions using a string-inspired first-quantized approach. Here we describe how to employ suitable particle actions in the computation of the scalar contribution to the one-loop gluon effective action. We use the well-known method of introducing auxiliary variables that create the color degrees of freedom. In a path integral they implement automatically the path ordering needed to ensure gauge invariance. It is known that the color degrees of freedom introduced this way form a reducible representation of the gauge group. We describe a method of projecting onto the fundamental representation (or any other chosen irrep, if desired) of the gauge group. Previously, we have discussed the case of anticommuting auxiliary variables. Choosing them to be in the fundamental representation allows to obtain, without any extra effort, also the situation in which the color is given by any antisymmetric tensor product of the fundamental. Here, we describe the novel case of bosonic auxiliary variables. They can be used equivalently for creating the color charges in the fundamental representation. In addition one gets, as a byproduct, the cases where the particle can have the color sitting in any symmetric tensor product of the fundamental. This is obtained by tuning to a different value a Chern Simons coupling, present in the model, which controls how the projection is achieved.

2019 - One-loop quantum gravity from the N particle 4 spinning [Articolo su rivista]
Bastianelli, F.; Bonezzi, R.; Corradini, O.; Latini, E.
abstract

We construct a spinning particle that reproduces the propagation of the gravi- ton on those curved backgrounds which solve the Einstein equations, with or without cosmological constant, i.e. Einstein manifolds. It is obtained by modifying the N = 4 supersymmetric spinning particle by relaxing the gauging of the full SO(4) R-symmetry group to a parabolic subgroup, and selecting suitable Chern-Simons couplings on the worldline. We test it by computing the correct one-loop divergencies of quantum gravity in D = 4.

2019 - Spinning particles and higher spin field equations [Relazione in Atti di Convegno]
Bastianelli, Fiorenzo; Bonezzi, Roberto; Corradini, Olindo; Latini, Emanuele
abstract

Relativistic particles with higher spin can be described in first quantization using actions with local supersymmetry on the worldline. First, we present a brief review of these actions and their use in first quantization. In a Dirac quantization scheme the field equations emerge as Dirac constraints on the Hilbert space, and we outline how they lead to the description of higher spin fields in terms of the more standard Fronsdal-Labastida equations. Then, we describe how these actions can be extended so that the propagating particle is allowed to take different values of the spin, i.e. carry a reducible representation of the Poincar ́e group. This way one may identify a four dimensional model that carries the same degrees of freedom of the minimal Vasiliev’s interacting higher spin field theory. Extensions to massive particles and to propagation on (A)dS spaces are also briefly commented upon.

2019 - U(N) Yang-Mills in non-commutative space time [Articolo su rivista]
Ahmadiniaz, Naser; Corradini, Olindo; Edwards, James P.; Pisani, Pablo
abstract

We present an approach to U ⋆ (N) Yang-Mills theory in non-commutative space based upon a novel phase-space analysis of the dynamical fields with additional auxiliary variables that generate Lorentz structure and colour degrees of freedom. To illustrate this formalism we compute the quadratic terms in the effective action focusing on the planar divergences so as to extract the β-function for the Yang-Mills coupling constant. Nonetheless the method presented is general and can be applied to calculate the effective action at arbitrary order of expansion in the coupling constant and is well suited to the computation of low energy one-loop scattering amplitudes.

2019 - Worldline formalism for a confined scalar field [Articolo su rivista]
Corradini, O.; Edwards, J. P.; Huet, I.; Manzo, L.; Pisani, P.
abstract

The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle whose transition amplitudes correspond to the heat-kernel of the operator of quantum fluctuations of the field theory. However, to study a quantum field which is confined within some boundaries one needs to restrict the path integration domain of the auxiliary point-particle to a specific subset of worldlines enclosed by those boundaries. We show how to implement this restriction for the case of a scalar field confined to the D-dimensional ball under Dirichlet and Neumann boundary conditions, and compute the first few heat-kernel coefficients as a verification of our construction. We argue that this approach could admit different generalizations.

2018 - Multiphoton amplitude in a constant background field [Relazione in Atti di Convegno]
Ahmad, Aftab; Ahmadiniaz, Naser; Corradini, Olindo; Pyo Kim, Sang; Schubert, Christian
abstract

In this contribution, we present our recent compact master formulas for the multiphoton amplitudes of a scalar propagator in a constant background field using the worldline fomulation of quantum field theory. The constant field has been included nonperturbatively, which is crucial for strong external fields. A possible application is the scattering of photons by electrons in a strong magnetic field, a process that has been a subject of great interest since the discovery of astrophysical objects like radio pulsars, which provide evidence that magnetic fields of the order of 1012G are present in nature. The presence of a strong external field leads to a strong deviation from the classical scattering amplitudes. We explicitly work out the Compton scattering amplitude in a magnetic field, which is a process of potential relevance for astrophysics. Our final result is compact and suitable for numerical integration.

2018 - Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo; Iacconi, Laura
abstract

Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the nonlinear kinetic term. Recently, for maximally symmetric spaces, simplified path integrals have been developed: they allow to trade the nonlinear kinetic term with a purely quadratic kinetic term (linear sigma model). This happens at the expense of introducing a suitable effective scalar potential, which contains the information on the curvature of the space. The simplified path integral provides a sensible gain in the efficiency of perturbative calculations. Here we extend the construction to models with N = 1 supersymmetry on the worldline, which are applicable to the first quantized description of a Dirac fermion. As an application we use the simplified worldline path integral to compute the type-A trace anomaly of a Dirac fermion in d dimensions up to d = 16.

2018 - String-inspired methods and the worldline formalism in curved space [Articolo su rivista]
Corradini, Olindo; Muratori, Maurizio
abstract

The worldline approach to Quantum Field Theory (QFT) allows to efficiently compute several quantities, such as one-loop effective actions, scattering amplitudes and anomalies, which are linked to particle path integrals on the circle. A helpful tool in the worldline formalism on the circle are string- inspired (SI) Feynman rules, which correspond to a specific way of factoring out a zero mode. In flat space this is known to generate no difficulties. In curved space, it was shown how to correctly achieve the zero mode factorization by applying BRST techniques to fix a shift symmetry. Using special coordinate systems, such as Riemann Normal Coordinates, implies the appearance of a non-linear map —originally introduced by Friedan— which must be taken care of in order to obtain the correct results. In particular, employing SI Feynman rules, the map introduces further interactions in the worldline path integrals. In the present paper, we compute in closed form Friedan’s map for RNC coordinates in maximally symmetric spaces, and test the path integral model by computing trace anomalies. Our findings match known results.

2018 - Worldline colour fields and non-Abelian quantum field theory [Relazione in Atti di Convegno]
Edwards, James; Corradini, Olindo
abstract

In the worldline approach to non-Abelian field theory the colour degrees of freedom of the coupling to the gauge potential can be incorporated using worldline “colour” fields. The colour fields generate Wilson loop interactions whilst Chern-Simons terms project onto an irreducible representation of the gauge group. We analyse this augmented worldline theory in phase space focusing on its supersymmetry and constraint algebra, arriving at a locally supersymmetric theory in superspace. We demonstrate canonical quantisation and the path integral on S1for simple representations of SU(N).

2017 - Master formulas for the dressed scalar propagator in a constant field [Articolo su rivista]
Ahmad, Aftab; Ahmadiniaz, Naser; Corradini, Olindo; Kim, Sang Pyo; Schubert, Christian
abstract

The worldline formalism has previously been used for deriving compact master formulas for the one-loop N-photon amplitudes in both scalar and spinor QED, and in the vacuum as well as in a constant external field. For scalar QED, there is also an analogous master formula for the propagator dressed with N photons in the vacuum. Here, we extend this master formula to include a constant field. The two-photon case is worked out explicitly, yielding an integral representation for the Compton scattering cross section in the field suitable for numerical integration in the full range of electric and magnetic field strengths.

2017 - On the simplified path integral on spheres [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo
abstract

We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the particle action. The emerging linear sigma model contains a scalar effective potential that reproduces the effects of the curvature. We present here further details of the construction, and extend its perturbative evaluation to orders high enough to read off the type-A trace anomalies of a conformal scalar in dimensions d= 14 and d= 16.

2017 - One-particle reducible contribution to the one-loop spinor propagator in a constant field [Articolo su rivista]
Ahmadiniaz, Naser; Bastianelli, Fiorenzo; Corradini, Olindo; Edwards, James P; Schubert, Christian
abstract

Extending work by Gies and Karbstein on the Euler–Heisenberg Lagrangian, it has recently been shown that the one-loop propagator of a charged scalar particle in a constant electromagnetic field has a one-particle reducible contribution in addition to the well-studied irreducible one. Here we further generalize this result to the spinor case, and find the same relation between the reducible term, the tree-level propagator and the one-loop Euler–Heisenberg Lagrangian as in the scalar case. Our demonstration uses a novel worldline path integral representation of the photon-dressed spinor propagator in a constant electromagnetic field background.

2017 - Quantum mechanical path integrals in curved spaces and the type-A trace anomaly [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo; Vassura, Edoardo
abstract

Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in arbitrary coordi- nates is well understood, and known to require the use of a regularization scheme, in this article we take up an old proposal of constructing the path integral by using Riemann nor- mal coordinates. The method assumes that curvature effects are taken care of by a scalar effective potential, so that the particle lagrangian is reduced to that of a linear sigma model interacting with the effective potential. After fixing the correct effective potential, we test the construction on spaces of maximal symmetry and use it to compute heat kernel coef- ficients and type-A trace anomalies for a scalar field in arbitrary dimensions up to d = 12. The results agree with expected ones, which are reproduced with great efficiency and ex- tended to higher orders. We prove explicitly the validity of the simplified path integral on maximally symmetric spaces. This simplified path integral might be of further use in world- line applications, though its application on spaces of arbitrary geometry remains unclear.

2017 - Quantum mechanics and hidden superconformal symmetry [Articolo su rivista]
Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.
abstract

Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp(1|2) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp(1|2) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models - both oscillator and particlelike - realize all possible unitary irreducible representations of osp(1|2).

2016 - Dressed scalar propagator in a non-Abelian background from the worldline formalism [Articolo su rivista]
Ahmadiniaz, Naser; Bastianelli, Fiorenzo; Corradini, Olindo
abstract

We study the propagator of a colored scalar particle in the background of a non-abelian gauge field using the worldline formalism. It is obtained by considering the open worldline of a scalar particle with extra degrees of freedom needed to take into account the color charge of the particle, which we choose to be in the fundamental representation of the gauge group. Specializing the external gauge field to be given by a sum of plane waves, i.e. a sum of external gluons, we produce a master formula for the scalar propagator with an arbitrary number of gluons directly attached to the scalar line, akin to similar formulas derived in the literature for the case of the scalar particle performing a loop. Our worldline description produces at the same time the situation in which the particle has a color charge given by an arbitrarily chosen symmetric or antisymmetric tensor product of the fundamental.

2016 - Erratum: Dressed scalar propagator in a non-Abelian background from the worldline formalism (Physical Review D - Particles, Fields, Gravitation and Cosmology (2016) 93 (025035)) [Articolo su rivista]
Ahmadiniaz, N.; Bastianelli, F.; Corradini, O.
abstract

2016 - Gravitational Compton Scattering from the Worldline Formalism [Relazione in Atti di Convegno]
Ahmadiniaz, Naser; Corradini, Olindo; Davila, Jose Manuel; Schubert, Christian
abstract

We report on an ongoing study of photon amplitudes, graviton amplitudes and mixed photon-graviton amplitudes at tree-level using the worldline formalism. We explicitly recalculate the amplitude with one photon and one graviton coupled to a scalar propagator, relevant for graviton photoproduction. We comment on the factorization properties of this amplitude, and outline a generalization to similar processes involving more gravitons.

2016 - Mixed symmetry tensors in the worldline formalism [Articolo su rivista]
Corradini, Olindo; Edwards, James P.
abstract

We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) “flavour” symmetry on the world- line particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation num- bers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We sug- gest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.

2016 - Mixed symmetry Wilson-loop interactions in the worldline formalism [Articolo su rivista]
Edwards, James P; Corradini, Olindo
abstract

Using the worldline formalism of the Dirac field with a non-Abelian gauge symmetry we show how to describe the matter field transforming in an arbitrary representation of the gauge group. Colour degrees of freedom are carried on the worldline by auxiliary fields, responsible for providing path ordering and the Wilson-loop coupling. The Hilbert space of these fields is reducible but we make use of recent work in order to project onto a single, arbitrary, irreducible representation. By functionally quantising the resulting theory we show that this procedure correctly generates the Wilson-loop interaction between the gauge field and the matter field taken to transform in a chosen representation. This work has direct application to physical observables such as scattering amplitudes in the presence of such a matter multiplet and lifts the restriction on the type of matter that has previously featured in worldline calculations.

2015 - Localization of abelian gauge fields on thick branes [Articolo su rivista]
Vaquera Araujo, Carlos A.; Corradini, Olindo
abstract

In this work, we explore a mechanism for abelian gauge field localization on thick branes based on a five-dimensional Stueckelberg-like action. A normalizable zero mode is found through the identification of a suitable coupling function between the brane and the gauge field. The same mechanism is studied for the localization of the abelian Kalb--Ramond field.

2015 - Noncommutative U(1) gauge theory from a worldline perspective [Articolo su rivista]
Naser, Ahmadiniaz; Corradini, Olindo; D'Ascanio, Daniela; Estrada Jimenez, Sendic; Pisani, Pablo
abstract

We study pure noncommutative U(1) gauge theory representing its one-loop effective action in terms of a phase space worldline path integral. We write the quadratic action using the background field method to keep explicit gauge invariance, and then employ the worldline formalism to write the one-loop effective action, singling out UV-divergent parts and finite (planar and non-planar) parts, and study renormalization properties of the theory. This amounts to employ worldline Feynman rules for the phase space path integral, that nicely incorporate the Fadeev-Popov ghost contribution and efficiently separate planar and non-planar contributions. We also show that the effective action calculation is independent of the choice of the worldline Green's function, that corresponds to a particular way of factoring out a particle zero-mode. This allows to employ homogeneous string-inspired Feynman rules that greatly simplify the computation.

2015 - Quantum gravity and causal structures: Second quantization of conformal Dirac algebras [Articolo su rivista]
Bonezzi, R.; Corradini, Olindo; Latini, E.; Waldron, A.
abstract

It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum gravity models by quantizing the moduli of Laplace, weight, and defining-function operators on Fefferman–Graham ambient spaces. The algebra of these operators underlies conformal geometries. We extend those results to include fermions by taking an osp(1j2) “Dirac square root” of these algebras. The theory is a simple, Grassmann, two-matrix model. Its quantum action is a Chern–Simons theory whose differential is a first-quantized, quantum mechanical Becchi-Rouet-Stora-Tyutin operator. The theory is a basic ingredient for building fundamental theories of physical observables.

2015 - Topological invariants in interacting quantum spin Hall: a cluster perturbation theory approach [Articolo su rivista]
Grandi, F.; Manghi, Franca; Corradini, Olindo; Bertoni, Carlo Maria; Bonini, Alfredo
abstract

Using cluster perturbation theory we calculate Greenʼs functions, quasi-particle energies and topological invariants for interacting electrons on a 2Dhoneycomb lattice, with intrinsic spin–orbit coupling and on-site e–e interaction. This allows us to define the parameter range (HubbardUversus spin– orbit coupling) where the 2D system behaves as a trivial insulator or quantum spin Hall insulator. This behavior is confirmed by the existence of gapless quasi-particle states in honeycomb ribbons.Wehave discussed the importance of the cluster symmetry and the effects of the lack of full translation symmetry typical of CPT and of most quantum cluster approaches. Comments on the limits of applicability of the method are also provided.

2015 - Topological properties of the bond-modulated honeycomb lattice [Articolo su rivista]
Grandi, F.; Manghi, Franca; Corradini, Olindo; Bertoni, Carlo Maria
abstract

We study the combined effects of lattice deformation, e−e interaction, and spin-orbit coupling in a two-dimensional (2D) honeycomb lattice. We adopt different kinds of hopping modulation—generalized dimerization and a Kekulé distortion—and calculate topological invariants for the noninteracting system and for the interacting system. We identify the parameter range (Hubbard U, hopping modulation, spin-orbit coupling) where the 2D system behaves as a trivial insulator or quantum spin Hall insulator.

2014 - Is quantum gravity a Chern-Simons theory? [Articolo su rivista]
Bonezzi, R.; Corradini, Olindo; Waldron, A.
abstract

We propose a model of quantum gravity in arbitrary dimensions defined in terms of the Batalin Vilkovisky (BV) quantization of a supersymmetric, infinite dimensional matrix model. This gives an Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ)-type Chern-Simons theory with gauge algebra the space of observables of a quantum mechanical Hilbert space H. The model is motivated by previous attempts to formulate gravity in terms of noncommutative, phase space, field theories as well as the Fefferman-Graham (FG) curved analog of Dirac spaces for conformally invariant wave equations. The field equations are flat connection conditions amounting to zero curvature and parallel conditions on operators acting on H. This matrix-type model may give a better defined setting for a quantum gravity path integral. We demonstrate that its underlying physics is a summation over Hamiltonians labeled by a conformal class of metrics and thus a sum over causal structures. This gives in turn a model summing over fluctuating metrics plus a tower of additional modes—we speculate that these could yield improved UV behavior.

2014 - Massive and massless higher spinning particles in odd dimensions [Articolo su rivista]
Bastianelli, Fiorenzo; Bonezzi, Roberto; Corradini, Olindo; Latini, Emanuele
abstract

Abstract: We study actions for massive bosonic particles of higher spins by dimensionally reducing an action for massless particles. For the latter we take a model with a SO(N) extended local supersymmetry on the worldline, that is known to describe massless (confor- mal) particles of higher spins in flat spacetimes of even dimensions. Dimensional reduction produces an action for massive spinning particles in odd dimensions. The field equations that emerge in a quantization `a la Dirac are shown to be equivalent to the Fierz-Pauli ones. The massless limit generates a multiplet of massless states with higher spins, whose first quantized field equations have a geometric form with fields belonging to various types of Young tableaux. These geometric equations can be partially integrated to show their equiv- alence with the standard Fronsdal-Labastida equations. We covariantize our model to check whether an extension to curved spacetimes can be achieved. Restricting to (A)dS spaces, we find that the worldline gauge algebra becomes nonlinear, but remains first class. This guar- antees consistency on such backgrounds. A light cone analysis confirms the presence of the expected propagating degrees of freedom. A covariant analysis is worked out explicitly for the massive case, which is seen to give rise to the Fierz-Pauli equations extended to (A)dS spaces. It is worth noting that in D = 3 the massless limit of our model with N → ∞ has the same field content of the Vasiliev’s theory that accommodates each spin exactly once.

2013 - On the galactic rotation curves problem within an axisymmetric approach [Articolo su rivista]
Herrera Aguilar, A.; Nucamendi, U.; Santos, E.; Corradini, Olindo; Alvarez, C.
abstract

In U. Nucamendi et al. Phys. Rev. D63 (2001) 125016 and K. Lake, Phys. Rev. Lett. 92 (2004) 051101 it has been shown that galactic potentials can be kinematically linked to the observed red/blue shifts of the corresponding galactic rotation curves under a minimal set of assumptions: the emitted photons come from stable timelike circular geodesic orbits of stars in a static spherically symmetric gravitational field, and propagate to us along null geodesics. It is remarkable that this relation can be established without appealing at all to a concrete theory of gravitational interaction. Here we generalize this kinematical spherically symmetric approach to the galactic rotation curves problem to the stationary axisymmetric realm since this is precisely the symmetry that spiral galaxies possess. Thus, by making use of the most general stationary axisymmetric metric, we also consider stable circular orbits of stars that emit signals which travel to a distant observer along null geodesics and express the galactic red/blue shifts in terms of three arbitrary metric functions, clarifying the contribution of the rotation as well as the dragging of the gravitational field. This stationary axisymmetric approach distinguishes between red and blue shifts emitted by circularly orbiting receding and approaching stars, respectively, even when they are considered with respect to the center of a spiral galaxy, indicating the need of precise measurements in order to confront predictions with observations. We also point out the difficulties one encounters in the attempt of determining the metric functions from observations and list some possible strategies to overcome them.

2013 - Particles with non abelian charges [Articolo su rivista]
Bastianelli, Fiorenzo; Bonezzi, Roberto; Corradini, Olindo; Latini, Emanuele
abstract

Efficient methods for describing non abelian charges in worldline approaches to QFT are useful to simplify calculations and address structural properties, as for example color/kinematics relations. Here we analyze in detail a method for treating arbitrary non abelian charges. We use Grassmann variables to take into account color degrees of freedom, which however are known to produce reducible representations of the color group. Then we couple them to a U(1) gauge field defined on the worldline, together with a Chern-Simons term, to achieve projection on an irreducible representation. Upon gauge fixing there remains a modulus, an angle parametrizing the U(1) Wilson loop, whose dependence is taken into account exactly in the propagator of the Grassmann variables. We test the method in simple examples, the scalar and spin 1/2 contribution to the gluon self energy, and suggest that it might simplify the analysis of more involved amplitudes.

2013 - Photon-graviton amplitudes [Relazione in Atti di Convegno]
Ahmadiniaz, N.; Bastianelli, F.; Corradini, Olindo; Dávila, José M.; Schubert, C.
abstract

We report on an ongoing study of the one-loop photon-graviton amplitudes, using both effective action and worldline techniques. The emphasis is on Kawai-Lewellen-Tye-like relations.

2012 - Effective action for higher spin fields on (A)dS backgrounds [Articolo su rivista]
Bastianelli, Fiorenzo; Bonezzi, Roberto; Corradini, Olindo; Latini, Emanuele
abstract

We study the one loop effective action for a class of higher spin fields by using a first-quantized description. The latter is obtained by considering spinning particles, characterized by an extended local supersymmetry on the worldline, that can propagate consistently on conformally flat spaces. The gauge fixing procedure for calculating the worldline path integral on a loop is delicate, as the gauge algebra contains nontrivial structure functions. Restricting the analysis on (A)dS backgrounds simplifies the gauge fixing procedure, and allows us to produce a useful representation of the one loop effective action. In particular, we extract the first few heat kernel coefficients for arbitrary even spacetime dimension D and for spin S identified by a curvature tensor with the symmetries of a rectangular Young tableau of D/2 rows and [S] columns.

2012 - Local unit invariance, back-reacting tractors and the cosmological constant problem [Relazione in Atti di Convegno]
Bonezzi, R.; Corradini, O.; Waldron, A.
abstract

When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.

2012 - On the low-energy limit of one-loop photon–graviton amplitudes [Articolo su rivista]
Bastianelli, F.; Corradini, Olindo; Dávila, J. M.; Schubert, C.
abstract

We present first results of a systematic study of the structure of the low energy limit of the one-loop photon-graviton amplitudes induced by massive scalars and spinors. Our main objective is the search of KLT-type relations where effectively two photons merge into a graviton. We find such a relation at the graviton-photon-photon level. We also derive the diffeomorphism Ward identity for the 1PI one graviton - N photon amplitudes.

2012 - Photon-graviton amplitudes from the effective action [Articolo su rivista]
Bastianelli, F.; Corradini, O.; Davila, J. M.; Schubert, C.
abstract

We report on the status of an ongoing effort to calculate the complete one-loop low-energy effective actions in Einstein-Maxwell theory with a massive scalar or spinor loop, and to use them for obtaining the explicit form of the corresponding M-graviton/N-photon amplitudes. We present explicit results for the effective actions at the one-graviton four-photon level, and for the amplitudes at the one-graviton two-photon level. As expected on general grounds, these amplitudes relate in a simple way to the corresponding four-photon amplitudes. We also derive the gravitational Ward identity for the 1PI one-graviton-N photon amplitude. © 2012 Pleiades Publishing, Ltd.

2012 - Worldline approach to noncommutative field theory [Articolo su rivista]
Bonezzi, R; Corradini, Olindo; Viñas, S. A. Franchino; Pisani, P. A. G.
abstract

The study of the heat-trace expansion in noncommutative field theory has shown the existence of Moyal nonlocal Seeley-DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We show that these models can be studied in a worldline approach implemented in phase space and arrive to a master formula for the $n$-point contribution to the heat-trace expansion. This formulation could be useful in understanding some open problems in this area, as the heat-trace expansion for the noncommutative torus or the introduction of renormalizing terms in the action, as well as for generalizations to other nonlocal operators.

2012 - Z4flavor model in Randall-Sundrum model 1 [Articolo su rivista]
Alvarado, Carlos; Aranda, Alfredo; Corradini, Olindo; Rojas, Alma D.; Santos Rodriguez, Eli
abstract

Randall Sundrum models provide a possible explanation of (gauge-gravity) hierarchy, whereas discrete symmetry flavor groups yield a possible description of the texture of Standard Model fermion masses. We use both these ingredients to propose a five-dimensional extension of the Standard Model where the mass hierarchy of the four-dimensional effective field theory is obtained only using localizations parameters of order 1. We consider a bulk custodial gauge symmetry group together with an Abelian $Z_4$ group: the model turns out to yield a rather minimal extension of the SM as it only requires two brane Higgs fields to provide the desired Yukawa interactions and the required spontaneous symmetry breaking pattern. In fact, the presence of an extra-dimension allows the use of the Scherk-Schwarz mechanism to contribute to the breaking of the bulk custodial group down to the SM gauge symmetry. Moreover, no right-handed neutrinos are present and neutrino masses are generated radiatively with the help of a bulk charged scalar field that provides the Lepton-number violation. Using experimental inputs from the Global Neutrino Analysis and recent Daya Bay results, a numerical analysis is performed and allowed parameter regions are displayed.

2011 - Extended SUSY quantum mechanics: transition amplitudes and path integrals [Articolo su rivista]
Bastianelli, Fiorenzo; Bonezzi, Roberto; Corradini, Olindo; Latini, Emanuele
abstract

Quantum mechanical models with extended supersymmetry find interesting applications in worldline approaches to relativistic field theories. In this paper we consider one-dimensional nonlinear sigma models with O(N) extended supersymmetry on the worldline, which are used in the study of higher spin fields on curved backgrounds. We calculate the transition amplitude for euclidean times (i.e. the heat kernel) in a perturbative expansion, using both canonical methods and path integrals. The latter are constructed using three different regularization schemes, and the corresponding counterterms that ensure scheme independence are explicitly identified.

2011 - Spinning particle approach to higher spin field theory [Abstract in Rivista]
Corradini, O.
abstract

We shortly review on the connection between higher-spin gauge field theories and supersymmetric spinning particle models. In such approach the higher spin equations of motion are linked to the first-class constraint algebra associated with the quantization of particle models. Here we consider a class of spinning particle models characterized by local O(N)-extended supersymmetry since these models are known to provide an alternative approach to the geometric formulation of higher spin field theory. We describe the canonical quantization of the models in curved target space and discuss the obstructions that appear in presence of an arbitrarily curved background. We then point out the special role that conformally flat spaces appear to have in such models and present a derivation of the higher-spin curvatures for maximally symmetric spaces.

2010 - Half-integer higher spin fields in (A)dS from spinning particle models [Articolo su rivista]
Corradini, Olindo
abstract

We make use of O(2r+1) spinning particle models to construct linearized higher-spin curvatures in (A)dS spaces for fields of arbitrary half-integer spin propagating in a space of arbitrary (even) dimension: the field potentials, whose curvatures are computed with the present models, are spinor-tensors of mixed symmetry corresponding to Young tableaux with D/2 - 1 rows and r columns, thus reducing to totally symmetric spinor-tensors in four dimensions. The paper generalizes similar results obtained in the context of integer spins in (A)dS.

2010 - Smooth tensionful higher-codimensional brane worlds with bulk and brane form fields [Articolo su rivista]
Corradini, Olindo
abstract

Completely regular tensionful codimension-n brane world solutions are discussed, where the core of the brane is chosen to be a thin codimension-(n-1) shell in an infinite volume flat bulk, and an Einstein-Hilbert term localized on the brane is included (Dvali-Gabadadze-Porrati models). In order to support such localized sources we enrich the vacuum structure of the brane by the inclusion of localized form fields. We find that phenomenological constraints on the size of the internal core seem to impose an upper bound to the brane tension. Finite transverse-volume smooth solutions are also discussed.

2009 - Detours and paths: BRST complexes and worldline formalism [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo; Waldron, Andrew
abstract

We construct detour complexes from the BRST quantization of worldline diffeomorphism invariant systems. This yields a method to efficiently extract physical quantum field theories from particle models with first class constraint algebras. As an example, we show how to obtain the Maxwell detour complex by gauging N=2 supersymmetric quantum mechanics in curved space. Then we concentrate on first class algebras belonging to a class of recently introduced orthosymplectic quantum mechanical models and give generating functions for detour complexes describing higher spins of arbitrary symmetry types. The first quantized approach facilitates quantum calculations and we employ it to compute the number of physical degrees of freedom associated to the second quantized, field theoretical actions.

2009 - Simulating stochastic dynamics using large time steps [Articolo su rivista]
Corradini, Olindo; Faccioli, P; Orland, H.
abstract

We present an approach to investigate the long-time stochastic dynamics of multidimensional classical systems, in contact with a heat bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short- and long-time scales and both molecular dynamics or Monte Carlo (MC) simulations are generally inefficient. Using a field theoretic approach, we perform analytically the average over the short-time stochastic fluctuations. This way, we obtain an effective theory, which generates the same long-time dynamics of the original theory, but has a lower time-resolution power. Such an approach is used to develop an improved version of the MC algorithm, which is particularly suitable to investigate the dynamics of rare conformational transitions. In the specific case of molecular systems at room temperature, we show that elementary integration time steps used to simulate the effective theory can be chosen a factor approximately 100 larger than those used in the original theory. Our results are illustrated and tested on a simple system, characterized by a rugged energy landscape.

2008 - Induced gravity on intersecting brane worlds. II. Cosmology [Articolo su rivista]
Corradini, Olindo; Koyama, Kazuya; Tasinato, Gianmassimo
abstract

We explore cosmology of intersecting braneworlds with induced gravity on the branes. We find the cosmological equations that control the evolution of a moving codimension one brane and a codimension two brane that sits at the intersection. We study the Friedmann equation at the intersection, finding new contributions from the six dimensional bulk. These higher dimensional contributions allow us to find new examples of self-accelerating configurations for the codimension two brane at the intersection and we discuss their features.

2008 - Induced gravity on intersecting brane worlds: Maximally symmetric solutions [Articolo su rivista]
Corradini, Olindo; Koyama, Kazuya; Tasinato, Gianmassimo
abstract

We explore models of intersecting brane-worlds with induced gravity terms on codimension one branes and on their intersection. Maximally symmetric solutions for the branes and the intersection are found. We find new self-accelerating solutions. In a 6d spacetime, the solutions realize the see-saw modification of gravity where the UV scale of the modification to 4d gravity is determined by 6d Planck scale given by $M_6 \sim 10^-3$eV and the IR scale of the modification is determined by $M_6^2/M_4 \sim H_0 \sim 10^-42$ GeV where $H_0$ is present-day Hubble scale. We find that it is increasingly difficult to construct phenomenologically viable models in higher-dimensional spacetime due to the necessity to have the lower value for the fundamental Planck scale to realize the late time acceleration. It is found that the system also admits self-tuning solutions where the tension at the intersection does not change the geometry of the intersection. The induced gravity terms can avoid the necessity to compactify the extra dimensions. Finally, we discuss the possibility to have ordinary matter at the intersection, without introducing any regularisation, using the induced gravity terms.

2008 - Scalar field with Robin boundary conditions in the worldline formalism [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G.
abstract

The worldline formalism has been widely used to compute physical quantities in quantum field theory. However, applications of this formalism to quantum fields in the presence of boundaries have been studied only recently. In this article we show how to compute in the worldline approach the heat kernel expansion for a scalar field with boundary conditions of Robin type. In order to describe how this mechanism works, we compute the contributions due to the boundary conditions to the coefficients A_1, A_3/2 and A_2 of the heat kernel expansion of a scalar field on the positive real line.

2008 - Scalar heat kernel with boundary in the worldline formalism [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G; Schubert, Christian
abstract

The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this formalism has turned out to be a difficult problem. Recently, such a generalization was developed for the case of a scalar field on the half-space R_+ x R^D-1, based on an extension of the associated worldline path integral to the full R^D using image charges. We present here an improved version of this formalism which allows us to write down non-recursive master formulas for the n-point contribution to the heat kernel trace of a scalar field on the half-space with Dirichlet or Neumann boundary conditions. These master formulas are suitable to computerization. We demonstrate the efficiency of the formalism by a calculation of two new heat-kernel coefficients for the half-space, a_4 and a_9/2.

2008 - Spinning particles and higher spin fields on (A)dS backgrounds [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo; Latini, Emanuele
abstract

Spinning particle models can be used to describe higher spin fields in first quantization. In this paper we discuss how spinning particles with gauged O(N) supersymmetries on the worldline can be consistently coupled to conformally flat spacetimes, both at the classical and at the quantum level. In particular, we consider canonical quantization on flat and on (A)dS backgrounds, and discuss in detail how the constraints due to the worldline gauge symmetries produce geometrical equations for higher spin fields, i.e. equations written in terms of generalized curvatures. On flat space the algebra of constraints is linear, and one can integrate part of the constraints by introducing gauge potentials. This way the equivalence of the geometrical formulation with the standard formulation in terms of gauge potentials is made manifest. On (A)dS backgrounds the algebra of constraints becomes quadratic, nevertheless one can use it to extend much of the previous analysis to this case. In particular, we derive general formulas for expressing the curvatures in terms of gauge potentials and discuss explicitly the cases of spin 2, 3 and 4.

2008 - Trace anomaly inflation in brane-induced gravity [Articolo su rivista]
Corradini, Olindo; Iglesias, Alberto
abstract

In the present letter we find that Starobinsky's inflationary solution is also valid in the Dvali-Gabadadze-Porrati (DGP) model where a 3-brane is embedded in 5-dimensional Minkowski bulk. We show that such a solution is typically not supported by the Self-Accelerated branch of the model, giving therefore a natural selection of the conventional branch of solutions. In the absence of brane induced Einstein-Hilbert term the SA branch is always selected out. We then study the linearized modes around all such de Sitter brane solutions finding perturbative stability for a range of parameters of the brane QFT.

2007 - Higher spin fields from a worldline perspective [Articolo su rivista]
Fiorenzo, Bastianelli; Corradini, Olindo; Emanuele, Latini
abstract

Higher spin fields in four dimensions, and more generally conformal fields in arbitrary dimensions, can be described by spinning particle models with a gauged SO(N) extended supergravity on the worldline. We consider here the one-loop quantization of these models by studying the corresponding partition function on the one-dimensional torus. After gauge fixing the supergravity multiplet, the partition function reduces to an integral over the corresponding moduli space which is computed using orthogonal polynomial techniques. We obtain a compact formula which gives the number of physical degrees of freedom for all N in all dimensions. As an aside we compute the physical degrees of freedom of the SO(4) = SU(2)xSU(2) model with only a SU(2) factor gauged, which has attracted some interest in the literature.

2007 - Worldline approach to quantum field theories on flat manifolds with boundaries [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G.
abstract

We study a worldline approach to quantum field theories on flat manifolds with boundaries. We consider the concrete case of a scalar field propagating on R_+ x R^D-1 which leads us to study the associated heat kernel through a one dimensional (worldline) path integral. To calculate the latter we map it onto an auxiliary path integral on the full R^D using an image charge. The main technical difficulty lies in the fact that a smooth potential on R_+ x R^D-1 extends to a potential which generically fails to be smooth on R^D. This implies that standard perturbative methods fail and must be improved. We propose a method to deal with this situation. As a result we recover the known heat kernel coefficients on a flat manifold with geodesic boundary, and compute two additional ones, A_3 and A_7/2. The calculation becomes sensibly harder as the perturbative order increases, and we are able to identify the complete A_7/2 with the help of a suitable toy model. Our findings show that the worldline approach is viable on manifolds with boundaries. Certainly, it would be desirable to improve our method of implementing the worldline approach to further simplify the perturbative calculations that arise in the presence of non-smooth potentials.

2006 - Self-T-dual brane cosmology and the cosmological constant problem [Articolo su rivista]
Corradini, Olindo; Rinaldi, Massimiliano
abstract

We consider a codimension-one brane embedded in a gravity-dilaton bulk action, whose symmetries are compatible with T-duality along the space-like directions parallel to the brane, and the bulk time-like direction. The equations of motions in the string frame allow for a smooth background obtained by the union of two symmetric patches of AdS space. The Poincar\'e invariance of the solution appears to hold independently of the value of the brane vacuum energy, through a self-tuning property of the dilaton ground state. Moreover, the effective cosmology displays a bounce, at which the scale factor does not shrink to zero. Finally, by exploiting the T-duality symmetry, we show how to construct an ever-expanding Universe, along the lines of the Pre-Big Bang scenario.

2005 - 4D gravity on a brane from bulk higher-curvature terms [Articolo su rivista]
Corradini, Olindo
abstract

We study a gravity model where a tensionful codimension-one three-brane is embedded on a bulk with infinite transverse length. We find that 4D gravity is induced on the brane already at the classical level if we include higher-curvature (Gauss-Bonnet) terms in the bulk. Consistency conditions appear to require a negative brane tension as well as a negative coupling for the higher-curvature terms.

2004 - BRST treatment of zero modes for the worldline formalism in curved space [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo; Zirotti, Andrea
abstract

One-loop quantities in QFT can be computed in an efficient way using the worldline formalism. The latter rests on the ability of calculating 1D path integrals on the circle. In this paper we give a systematic discussion for treating zero modes on the circle of 1D path integrals for both bosonic and supersymmetric nonlinear sigma models, following an approach originally introduced by Friedan. We use BRST techniques and place a special emphasis on the issue of reparametrization invariance. Various examples are extensively analyzed to verify and test the general set-up. In particular, we explicitly check that the chiral anomaly, which can be obtained by the semiclassical approximation of a supersymmetric 1D path integral, does not receive higher order worldline contributions, as implied by supersymmetry.

2003 - Diluting solutions of the cosmological constant problem [Articolo su rivista]
Corradini, Olindo; Iglesias, Alberto; Kakushadze, Zurab
abstract

We discuss the cosmological constant problem in the context of higher codimension brane world scenarios with infinite-volume extra dimensions.

2003 - Dimensional regularization for N= 1 supersymmetric sigma models and the worldline formalism [Articolo su rivista]
Bastianelli, F.; Corradini, O.; Zirotti, A.
abstract

We generalize the worldline formalism to include spin 1/2 fields coupled to gravity. To this purpose we first extend dimensional regularization to supersymmetric nonlinear sigma models in one dimension. We consider a finite propagation time and find that dimensional regularization is a manifestly supersymmetric regularization scheme, since the classically supersymmetric action does not need any counterterm to preserve worldline supersymmetry. We apply this regularization scheme to the worldline description of Dirac fermions coupled to gravity. We first compute the trace anomaly of a Dirac fermion in 4 dimensions, providing an additional check on the regularization with finite propagation time. Then we come to the main topic and consider the one-loop effective action for a Dirac field in a gravitational background. We describe how to represent this effective action as a worldline path integral and compute explicitly the one- and two-point correlation functions, i.e. the spin 1/2 particle contribution to the graviton tadpole and graviton self-energy. These results are presented for the general case of a massive fermion. It is interesting to note that in the worldline formalism the coupling to gravity can be described entirely in terms of the metric, avoiding the introduction of a vielbein. Consequently, the fermion-graviton vertices are always linear in the graviton, just like the standard coupling of fermions to gauge fields. © 2003 The American Physical Society.

2003 - Dimensional regularization for N=1supersymmetric sigma models and the worldline formalism [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo; Zirotti, Andrea
abstract

We generalize the worldline formalism to include spin 1/2 fields coupled to gravity. To this purpose we first extend dimensional regularization to supersymmetric nonlinear sigma models in one dimension. We consider a finite propagation time and find that dimensional regularization is a manifestly supersymmetric regularization scheme, since the classically supersymmetric action does not need any counterterm to preserve worldline supersymmetry. We apply this regularization scheme to the worldline description of Dirac fermions coupled to gravity. We first compute the trace anomaly of a Dirac fermion in 4 dimensions, providing an additional check on the regularization with finite propagation time. Then we come to the main topic and consider the one-loop effective action for a Dirac field in a gravitational background. We describe how to represent this effective action as a worldline path integral and compute explicitly the one- and two-point correlation functions, i.e. the spin 1/2 particle contribution to the graviton tadpole and graviton self-energy. These results are presented for the general case of a massive fermion. It is interesting to note that in the worldline formalism the coupling to gravity can be described entirely in terms of the metric, avoiding the introduction of a vielbein. Consequently, the fermion--graviton vertices are always linear in the graviton, just like the standard coupling of fermions to gauge fields.

2003 - Toward solving the cosmological constant problem? [Articolo su rivista]
Corradini, Olindo; Iglesias, Alberto; Kakushadze, Zurab
abstract

We discuss the cosmological constant problem in the context of higher codimension brane world scenarios with infinite-volume extra dimensions. In particular, by adding higher curvature terms in the bulk action we are able to find smooth solutions with the property that the 4-dimensional part of the brane world-volume is flat for a range of positive values of the brane tension.

2002 - A remark on smoothing out higher codimension branes [Articolo su rivista]
Corradini, Olindo; Iglesias, Alberto; Kakushadze, Zurab; Langfelder, Peter
abstract

We discuss some issues arising in studying (linearized) gravity on non-BPS higher codimension branes in an infinite-volume bulk. In particular, such backgrounds are badly singular for codimension-3 and higher delta-function-like branes with non-zero tension. As we discuss in this note, non-trivial issues arise in smoothing out such singularities. Thus, adding higher curvature terms might be necessary in this context.

2001 - A remark on nonconformal nonsupersymmetric theories with vanishing vacuum energy density [Articolo su rivista]
Corradini, Olindo; Iglesias, Alberto; Kakushadze, Zurab; Langfelder, Peter
abstract

We discuss non-conformal non-supersymmetric large N gauge theories with vanishing vacuum energy density to all orders in perturbation theory. These gauge theories can be obtained via a field theory limit of Type IIB D3-branes embedded in orbifolded space-times. We also discuss gravity in this setup.

2001 - A solitonic 3-brane in 6D bulk [Articolo su rivista]
Corradini, Olindo; Kakushadze, Zurab
abstract

We construct a solitonic 3-brane solution in the 6-dimensional Einstein-Hilbert-Gauss-Bonnet theory with a (negative) cosmological term. This solitonic brane world is delta-function-like. Near the brane the metric is that for a product of the 4-dimensional flat Minkowski space with a 2-dimensional ``wedge'' with a deficit angle (which depends on the solitonic brane tension). Far from the brane the metric approaches that for a product of the 5-dimensional AdS space and a circle. This solitonic solution exists for a special value of the Gauss-Bonnet coupling (for which we also have a delta-function-like codimension-1 solitonic solution), and the solitonic brane tension can take values in a continuous range. We discuss various properties of this solitonic brane world, including coupling between gravity and matter localized on the brane.

2001 - Gravity on a 3-brane in 6D bulk [Articolo su rivista]
Corradini, Olindo; Iglesias, Alberto; Kakushadze, Zurab; Langfelder, Peter
abstract

We study gravity in codimension-2 brane world scenarios with infinite volume extra dimensions. In particular, we consider the case where the brane has non-zero tension. The extra space then is a two-dimensional ``wedge'' with a deficit angle. In such backgrounds we can effectively have the Einstein-Hilbert term on the brane at the classical level if we include higher curvature (Gauss-Bonnet) terms in the bulk. Alternatively, such a term would be generated at the quantum level if the brane matter is not conformal. We study (linearized) gravity in the presence of the Einstein-Hilbert term on the brane in such backgrounds. We find that, just as in the original codimension-2 Dvali-Gabadadze model with a tensionless brane, gravity is almost completely localized on the brane with ultra-light modes penetrating into the bulk.

2001 - 6D trace anomalies from quantum mechanical path integrals [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo
abstract

We use the recently developed dimensional regularization (DR) scheme for quantum mechanical path integrals in curved space and with a finite time interval to compute the trace anomalies for a scalar field in six dimensions. This application provides a further test of the DR method applied to quantum mechanics. It shows the efficiency in higher loop computations of having to deal with covariant counterterms only, as required by the DR scheme.

2000 - Dimensional regularization of nonlinear sigma models on a finite time interval [Articolo su rivista]
Bastianelli, F; Corradini, Olindo; Van Nieuwenhuizen, P.
abstract

We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'') dimensional regularization requires only a covariant finite two-loop counterterm. This counterterm is nonvanishing and given by R/8.

2000 - Dimensional regularization of the path integral in curved space on an infinite time interval [Articolo su rivista]
Bastianelli, F; Corradini, Olindo; Van Nieuwenhuizen, P.
abstract

We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general coordinates. It is shown that one only needs a covariant two-loop counterterm (V_{DR} = R/8) to obtain the same results as obtained earlier in other regularization schemes. It is also shown that the mass term needed in order to avoid infrared divergences explicitly breaks general covariance in the final result.

2000 - Localized gravity and higher curvature terms [Articolo su rivista]
Corradini, Olindo; Kakushadze, Zurab
abstract

We consider localization of gravity in smooth domain wall solutions of gravity coupled to a scalar field with a generic potential in the presence of the Gauss-Bonnet term. We discuss conditions on the scalar potential such that domain wall solutions are non-singular. We point out that the presence of the Gauss-Bonnet term does not allow flat solutions with localized gravity that violate the weak energy condition. We also point out that in the presence of the Gauss-Bonnet term infinite tension flat domain walls violate positivity. In fact, for flat solutions unitarity requires that on the solution the scalar potential be bounded below.

1999 - Mode regularization of the configuration space path integral in curved space [Articolo su rivista]
Bastianelli, Fiorenzo; Corradini, Olindo
abstract

The path integral representation of the transition amplitude for a particle moving in curved space has presented unexpected challenges since the introduction of path integrals by Feynman fifty years ago. In this paper we discuss and review mode regularization of the configuration space path integral, and present a three loop computation of the transition amplitude to test with success the consistency of such a regularization. Key features of the method are the use of the Lee-Yang ghost fields, which guarantee a consistent treatment of the non-trivial path integral measure at higher loops, and an effective potential specific to mode regularization which arises at two loops. We also perform the computation of the transition amplitude using the regularization of the path integral by time discretization, which also makes use of Lee-Yang ghost fields and needs its own specific effective potential. This computation is shown to reproduce the same final result as the one performed in mode regularization.

1997 - 't Hooft anomaly matching conditions for generalized symmetries in 2D [Articolo su rivista]
Bastianelli, F.; Corradini, Olindo
abstract

The 't Hooft anomaly matching conditions are a standard tool to study and test non-perturbative issues in quantum field theory. We give a new, simple proof of the anomaly matching conditions in 2D Poincare` invariant theories. We consider the case of invariance under a large class of generalized symmetries, which include abelian and non-abelian internal symmetries, space-time symmetries generated by the stress tensor, and W-type of symmetries generated by higher spin currents.