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DIEGO TRANCANELLI

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

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Pubblicazioni

2024 - Interpolating Bremsstrahlung function in ABJM [Articolo su rivista]
Castiglioni, L.; Penati, S.; Tenser, M.; Trancanelli, D.
abstract

In ABJM theory, enriched RG flows between circular 1/6 BPS bosonic and 1/2 BPS fermionic Wilson loops have been introduced in arXiv:2211.16501. These flows are triggered by deformations corresponding to parametric 1/6 BPS fermionic loops. In this paper we revisit the study of these operators, but instead of circular contours we consider an interpolating cusped line and a latitude and study their RG flow in perturbation theory. This allows for the definition of a Bremsstrahlung function away from fixed points. We generalize to this case the known cusp/latitude correspondence that relates the Bremsstrahlung function to a latitude Wilson loop. We find that away from the conformal fixed points the ordinary identity is broken by the conformal anomaly in a controlled way. From a defect perspective, the breaking of the correspondence can be traced back to the appearance of an anomalous dimension for fermionic operators localized on the defect. As a by-product, we provide a brand new result for the two-loop cusp anomalous dimension of the 1/6 BPS fermionic and the 1/6 BPS bosonic Wilson lines.

2023 - Interpolating Wilson loops and enriched RG flows [Articolo su rivista]
Castiglioni, Luigi; Penati, Silvia; Tenser, Marcia; Trancanelli, Diego
abstract

We study new 1/24 BPS circular Wilson loops in ABJ(M) theory, which are de- fined in terms of several parameters that continuously interpolate between previously known 1/6 BPS loops (both bosonic and fermionic) and 1/2 BPS fermionic loops. We compute the expectation value of these operators up to second order in perturbation theory using a one-dimensional effective field theory approach. Within dimensional regularization, we find non-trivial β-functions for the parameters, which are marginally relevant deformations triggering RG flows from a UV fixed point represented by the 1/6 BPS bosonic loop to an IR fixed point represented by a 1/2 BPS fermionic loop. Generically, along all flows at least one supercharge of the theory is preserved, so that we refer to them as enriched RG flows. In particular, fixed points are connected through 1/6 BPS fermionic operators. This holds at framing zero, which is a consequence of the regularization scheme employed. We also establish the validity of the g-theorem, relating the expectation values of the Wilson loops corresponding to the UV and IR fixed points of the flow, and discuss the one-dimensional defect SCFT living on the Wilson loop contour.

2023 - Topological Quantum Computation on Supersymmetric Spin Chains [Articolo su rivista]
Jana, I.; Montorsi, F.; Padmanabhan, P.; Trancanelli, D.
abstract

Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in SU(2)k quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising (k=2), Fibonacci (k=3) and Jones-Kauffman (k=4) anyons. We show that the fusion spaces of these anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains. As a result, we can realize the braid group on the product state zero modes of these supersymmetric systems. These operators kill all the other states in the Hilbert space, thus preventing the occurrence of errors while processing information, making them suitable for quantum computing.

2023 - Wilson loops and defect RG flows in ABJM [Articolo su rivista]
Castiglioni, L.; Penati, S.; Tenser, M.; Trancanelli, D.
abstract

We continue our study of renormalization group (RG) flows on Wilson loop defects in ABJM theory, which we have initiated in arXiv:2211.16501. We generalize that analysis by including non-supersymmetric fixed points and RG trajectories. To this end, we first determine the “ordinary", non-supersymmetric Wilson loops, which turn out to be two and to include an R-symmetry preserving coupling to the scalar fields of the theory, contrary to their four-dimensional counterpart defined solely in terms of the gauge field holonomy. We then deform these operators by turning on bosonic and/or fermionic couplings, which trigger an elaborate, multi-dimensional network of possible RG trajectories connecting a large spectrum of fixed points classified in terms of the amount (possibly zero) of supersymmetry and R-symmetry preserved. The β-functions are computed to leading order in the ABJM coupling but exactly in the deformation parameters, using an auxiliary one-dimensional theory on the defect and a dimensional regularization scheme. A striking result is the different behavior of the two ordinary Wilson loops, of which one turns out to be a UV unstable point while the other is IR stable. The same is true for the two 1/2 BPS Wilson loops. We interpret our results from a defect CFT (dCFT) point of view, computing the anomalous dimensions of the operators associated to the deformations and establishing appropriate g-theorems. In particular, the fermionic unstable fixed point is associated to a dCFT which is not reflection positive.

2022 - Classifying BPS bosonic Wilson loops in 3d N=4 Chern-Simons-matter theories [Articolo su rivista]
Drukker, Nadav; Kong, Ziwen; Probst, Malte; Tenser, Marcia; Trancanelli, Diego
abstract

We study the possible BPS Wilson loops in three-dimensional N = 4 Chern-Simons-matter theory which involve only the gauge field and bilinears of the scalars. Previously known examples are the analogues of the Gaiotto-Yin loops preserving four supercharges and “latitude” loops preserving two. We carry out a careful classification and find, in addition, loops preserving three supercharges, further inequivalent classes of loops preserving two supercharges and loops preserving a single supercharge. For each of the classes of loops, we present a representative example and analyse their full orbit under the broken symmetries.

2022 - Conformal and non-conformal hyperloop deformations of the 1/2 BPS circle [Articolo su rivista]
Drukker, N.; Kong, Z.; Probst, M.; Tenser, M.; Trancanelli, D.
abstract

We construct new large classes of BPS Wilson hyperloops in three-dimensional N=4 quiver Chern-Simons-matter theory on S3. The main strategy is to start with the 1/2 BPS Wilson loop of this theory, choose any linear combination of the supercharges it preserves, and look for deformations built out of the matter fields that still preserve that supercharge. This is a powerful generalization of a recently developed approach based on deformations of 1/4 and 1/8 BPS bosonic loops, which itself was far more effective at discovering new operators than older methods relying on complicated ansatze. We discover many new moduli spaces of BPS hyperloops preserving varied numbers of supersymmetries and varied subsets of the symmetries of the 1/2 BPS operator. In particular, we find new bosonic operators preserving 2 or 3 supercharges as well as new families of loops that do not share supercharges with any bosonic loops, including subclasses of both 1/8 and 1/4 BPS loops that are conformal.

2021 - Notes on hyperloops in N=4 Chern-Simons-matter theories [Articolo su rivista]
Drukker, Nadav; Marciatenser, ; Trancanelli, Diego
abstract

We present new circular Wilson loops in three-dimensional N=4 quiver Chern-Simons-matter theory on S3. At any given node of the quiver, a two-parameter family of operators can be obtained by opportunely deforming the 1/4 BPS Gaiotto-Yin loop. Including then adjacent nodes, the coupling to the bifundamental matter fields allows to enlarge this family and to construct loop operators based on superconnections. We discuss their classification, which depends on both discrete data and continuous parameters subject to an identification. The resulting moduli spaces are conical manifolds, similar to the conifold of the 1/6 BPS loops of the ABJ(M) theory.

2020 - Braiding quantum gates from partition algebras [Articolo su rivista]
Padmanabhan, P.; Sugino, F.; Trancanelli, D.
abstract

Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the (d,m,l)-generalized Yang-Baxter equation, for m/2≤l≤m, which allows to systematically construct such braiding operators. This is achieved by using partition algebras, a generalization of the Temperley-Lieb algebra encountered in statistical mechanics. We obtain families of unitary and non-unitary braiding operators that generate the full braid group. Explicit examples are given for a 2-, 3-, and 4-qubit system, including the classification of the entangled states generated by these operators based on Stochastic Local Operations and Classical Communication.

2020 - Generating W states with braiding operators [Articolo su rivista]
Padmanabhan, P.; Sugino, F.; Trancanelli, D.
abstract

Braiding operators can be used to create entangled states out of product states, thus establishing a correspondence between topological and quantum entanglement. This is well-known for maximally entangled Bell and GHZ states and their equivalent states under Stochastic Local Operations and Classical Communication, but so far a similar result for W states was missing. Here we use generators of extraspecial 2-groups to obtain the W state in a four-qubit space and partition algebras to generate the W state in a three-qubit space. We also present a unitary generalized Yang-Baxter operator that embeds the Wn state in a (2n-1)-qubit space.

2020 - Local invariants of braiding quantum gates -- associated link polynomials and entangling power [Articolo su rivista]
Padmanabhan, P.; Sugino, F.; Trancanelli, D.
abstract

For a generic n-qubit system, local invariants under the action of SL(2,C)⊗n characterize non-local properties of entanglement. In general, such properties are not immediately apparent and hard to construct. Here we consider two-qubit Yang-Baxter operators and show that their eigenvalues completely determine the non-local properties of the system. Moreover, we apply the Turaev procedure to these operators and obtain their associated link/knot polynomials. We also compute their entangling power and compare it with that of a generic two-qubit operator.

2020 - Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation [Articolo su rivista]
Padmanabhan, Pramod; Sugino, Fumihiko; Trancanelli, Diego
abstract

Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding operators as quantum entanglers, and is part of a larger speculated connection between topological and quantum entanglement. We push the analysis of this connection forward, by showing that supersymmetry algebras can be used to construct large families of solutions of the spectral parameter-dependent generalized Yang-Baxter equation. We present a number of explicit examples and outline a general algorithm for arbitrary numbers of qubits. The operators we obtain produce, in turn, all the entangled states in a multi-qubit system classified by the Stochastic Local Operations and Classical Communication protocol introduced in quantum information theory.

2020 - Roadmap on Wilson loops in 3d Chern-Simons-matter theories [Articolo su rivista]
Drukker, N.; Trancanelli, D.; Bianchi, L.; Bianchi, M. S.; Correa, D. H.; Forini, V.; Griguolo, L.; Leoni, M.; Levkovich-Maslyuk, F.; Nagaoka, G.; Penati, S.; Preti, M.; Probst, M.; Putrov, P.; Seminara, D.; Silva, G. A.; Tenser, M.; Trepanier, M.; Vescovi, E.; Yaakov, I.; Zhang, J.
abstract

This is a compact review of recent results on supersymmetric Wilson loops in ABJ(M) and related theories. It aims to be a quick introduction to the state of the art in the field and a discussion of open problems. It is divided into short chapters devoted to different questions and techniques. Some new results, perspectives and speculations are also presented. We hope this might serve as a baseline for further studies of this topic.

2019 - Deformations of the circular Wilson loop and spectral (in)dependence [Articolo su rivista]
Cooke, Michael; Dekel, Amit; Drukker, Nadav; Trancanelli, Diego; Vescovi, Edoardo
abstract

In this paper we study the expectation value of deformations of the circular Wilson loop in $cal N=4$ super Yang-Mills theory. The leading order deformation, known as the Bremsstrahlung function, can be obtained exactly from supersymmetric localization, so our focus is on deformations at higher orders. We find simple expressions for the expectation values for generic deformations at the quartic order at one-loop at weak coupling and at leading order at strong coupling. We also present a very simple algorithm (not requiring integration) to evaluate the two-loop result. We find that an exact symmetry of the strong coupling sigma-model, known as the spectral-parameter independence, is an approximate symmetry at weak coupling, modifying the expectation value starting only at the sextic order in the deformation. Furthermore, we find very simple patterns for how the spectral parameter can appear in the weak coupling calculation, suggesting all-order structures.

2018 - Supersymmetric integrable theories without particle production [Articolo su rivista]
Bercini, Carlos; Trancanelli, Diego
abstract

We consider a theory of scalar superfields in two dimensions with arbitrary superpotential. By imposing no particle production in tree level scattering, we constrain the form of the admissible interactions, recovering a supersymmetric extension of the sinh-Gordon model.

2017 - Quark-antiquark potential in defect conformal field theory [Articolo su rivista]
Preti, Michelangelo; Trancanelli, Diego; Vescovi, Edoardo
abstract

We consider antiparallel Wilson lines in N=4 super Yang-Mills in the presence of a codimension-1 defect. We compute the Wilson lines' expectation value both at weak coupling, in the gauge theory, and at strong coupling, by finding the string configurations which are dual to this operator. These configurations display a Gross-Ooguri transition between a connected, U-shaped string phase and a phase in which the string breaks into two disconnected surfaces. We analyze in detail the critical configurations separating the two phases and compare the string result with the gauge theory one in a certain double scaling limit.

2017 - Replica trick and string winding [Articolo su rivista]
Prudenziati, Andrea; Trancanelli, Diego
abstract

We apply the replica trick to compute the entropy of a cylinder amplitude in string theory. We focus on the contribution from non-perturbative winding modes and impose tadpole cancellation to understand the correct prescription for integrating over moduli. Choosing the entangling surface to cut longitudinally over the whole length of the cylinder, we obtain an answer that is interpreted as the entropy of a density matrix. We recast this result in target space language, both in the open and closed string picture.

2017 - Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling [Articolo su rivista]
Padmanabhan, Pramod; Rey, Soo-Jong; Teixeira, Daniel; Trancanelli, Diego
abstract

Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the index. The Hamiltonians we obtain are integrable and display a spectrum containing both product and entangled states. By introducing disorder and studying the out-of-time-ordered correlators (OTOC), we find that these systems are in the many-body localized phase and do not thermalize. Finally, we reformulate a theorem relating the growth of the second Renyi entropy to the OTOC on a thermal state in terms of partial symmetries.

2016 - Grandezas físicas e análise dimensional: da mecânica à gravidade quântica [Articolo su rivista]
Trancanelli, Diego
abstract

Physical quantities and physical dimensions are among the first concepts encountered by students in their undergraduate career. In this pedagogical review, I will start from these concepts and, using the powerful tool of dimensional analysis, I will embark in a journey through various branches of physics, from basic mechanics to quantum gravity. I will also discuss a little bit about the fundamental constants of Nature, the so-called "cube of Physics", and the natural system of units.

2016 - Thermodynamics of anisotropic branes [Articolo su rivista]
Ávila, Daniel; Fernández, Daniel; Patiño, Leonardo; Trancanelli, Diego
abstract

We study the thermodynamics of flavor D7-branes embedded in an anisotropic black brane solution of type IIB supergravity. The flavor branes undergo a phase transition between a `Minkowski embedding', in which they lie outside of the horizon, and a `black hole embedding', in which they fall into the horizon. This transition depends on the black hole temperature, its degree of anisotropy, and the mass of the flavor degrees of freedom. It happens either at a critical temperature or at a critical anisotropy. A general lesson we learn from this analysis is that the anisotropy, in this particular realization, induces similar effects as the temperature. In particular, increasing the anisotropy bends the branes more and more into the horizon. Moreover, we observe that the transition becomes smoother for higher anisotropies.

2016 - Toward precision holography with supersymmetric Wilson loops [Articolo su rivista]
Faraggi, Alberto; Pando Zayas, Leopoldo A.; Silva, Guillermo A.; Trancanelli, Diego
abstract

We consider certain 1/4 BPS Wilson loop operators in SU(N) N=4 supersymmetric Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in AdS5×S5. The string on-shell action reproduces the large N and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by deriving the spectrum of quantum fluctuations around the classical string solution and by computing the corresponding 1-loop effective action. We discuss in detail the supermultiplet structure of the fluctuations. To remove a possible source of ambiguity in the ghost zero mode measure, we compare the 1/4 BPS configuration with the 1/2 BPS one, dual to a circular Wilson loop. We find a discrepancy between the string theory result and the gauge theory prediction, confirming a previous result in the literature. We are able to track the modes from which this discrepancy originates, as well as the modes that by themselves would give the expected result.

2015 - A profusion of 1/2 BPS Wilson loops in N = 4 Chern-Simons-matter theories [Articolo su rivista]
Cooke, Michael; Drukker, Nadav; Trancanelli, Diego
abstract

We initiate the study of 1/2 BPS Wilson loops in N=4 Chern-Simons-matter theories in three dimensions. We consider a circular or linear quiver with Chern-Simons levels k, -k and 0, and focus on loops preserving one of the two SU(2) subgroups of the R-symmetry. In the cases with no vanishing Chern-Simons levels, we find a pair of Wilson loops for each pair of adjacent nodes on the quiver connected by a hypermultiplet (nodes connected by twisted hypermultiplets have Wilson loops preserving another set of supercharges). We expect this classical pairwise degeneracy to be lifted by quantum corrections. In the case with nodes with vanishing Chern-Simons terms connected by twisted hypermultiplets, we find that the usual 1/4 BPS Wilson loops are automatically enlarged to 1/2 BPS, as happens also in 3-dimensional Yang-Mills theory. When the nodes with vanishing Chern-Simons levels are connected by untwisted hypermultiplets, we do not find any Wilson loops coupling to those nodes which are classically invariant. Rather, we find several loops whose supersymmetry variation, while non zero, vanishes in any correlation function, so is weakly zero. We expect only one linear combination of those Wilson loops to remain BPS when quantum corrections are included. We analyze the M-theory duals of those Wilson loops and comment on their degeneracy. We also show that these Wilson loops are cohomologically equivalent to certain 1/4 BPS Wilson loops whose expectation value can be evaluated by the appropriate localized matrix model.

2015 - Cusped Wilson lines in symmetric representations [Articolo su rivista]
Correa, Diego H.; Massolo, Fidel I. Schaposnik; Trancanelli, Diego
abstract

We study the cusped Wilson line operators and Bremsstrahlung functions associated to particles transforming in the rank-k symmetric representation of the gauge group U(N) for N = 4 super Yang-Mills. We find the holographic D3-brane description for Wilson loops with internal cusps in two different limits: small cusp angle and k√λ≫ N. This allows for a non-trivial check of a conjectured relation between the Bremsstrahlung function and the expectation value of the 1/2 BPS circular loop in the case of a representation other than the fundamental. Moreover, we observe that in the limit of k≫ N, the cusped Wilson line expectation value is simply given by the exponential of the 1-loop diagram. Using group theory arguments, this eikonal exponentiation is conjectured to take place for all Wilson loop operators in symmetric representations with large k, independently of the contour on which they are supported.

2015 - Holographic renormalization and anisotropic black branes in higher curvature gravity [Articolo su rivista]
Jahnke, Viktor; Misobuchi, Anderson Seigo; Trancanelli, Diego
abstract

We consider five-dimensional AdS-axion-dilaton gravity with a Gauss-Bonnet term and find a solution of the equations of motion which corresponds to a black brane exhibiting a spatial anisotropy, with the source of the anisotropy being an axion field linear in one of the horizon coordinates. Our solution is static, regular everywhere on and outside the horizon, and asymptotically AdS. It is analytic and valid in a small anisotropy expansion, but fully non-perturbative in the Gauss-Bonnet coupling. We discuss various features of this solution and use it as a gravity dual to a strongly coupled anisotropic plasma with two independent central charges, a≠ c. In the limit of small Gauss-Bonnet coupling, we carry out holographic renormalization of the system using (a recursive variant of) the Hamilton-Jacobi method and derive a generic expression for the boundary stress tensor, which we later specialize to our solution. Finally, we compute the shear viscosity to entropy ratios and conductivities of this anisotropic plasma.

2014 - Chern-Simons diffusion rate from higher curvature gravity [Articolo su rivista]
Jahnke, Viktor; Misobuchi, Anderson Seigo; Trancanelli, Diego
abstract

An important transport coefficient in the study of non-Abelian plasmas is the Chern-Simons diffusion rate, which parameterizes the rate of transition among the degenerate vacua of a gauge theory. We compute this quantity at strong coupling, via holography, using two theories of gravity with higher curvature corrections, namely Gauss-Bonnet gravity and quasi-topological gravity. We find that these corrections may either increase or decrease the result obtained from Einstein's gravity, depending on the value of the couplings. The Chern-Simons diffusion rate for Gauss-Bonnet gravity decreases as the shear viscosity over entropy ratio is increased.

2014 - More on thermal probes of a strongly coupled anisotropic plasma [Articolo su rivista]
Jahnke, Viktor; Luna, Andrés; Patiño, Leonardo; Trancanelli, Diego
abstract

We extend the analysis of 1211.2199, where the photon production rate of an anisotropic strongly coupled plasma with Nf<

2014 - S-duality and the giant magnon dispersion relation [Articolo su rivista]
Berenstein, David; Trancanelli, Diego
abstract

We use S-duality and planarity to propose an argument for the non-renormalization of the dispersion relation of giant magnon solutions in type IIB string theory on AdS5×S5. We compute the spectrum of giant magnons for (p,q)-strings from field theory at strong coupling by using the central charge properties of electrically and magnetically charged supersymmetric states in the Coulomb branch of N=4 super Yang-Mills. We argue that the coupling dependence of the giant magnon dispersion relation conjectured in the literature using integrability assumptions is in fact the only functional dependence compatible with S-duality.

2013 - Observables of a strongly coupled anisotropic plasma [Altro]
Trancanelli, Diego
abstract

In this thesis we apply the gauge/gravity duality to the study of a strongly coupled plasma with a spatial anisotropy. After reviewing the type IIB supergravity solution dual to such a system, we compute various physi- cal observables of interest, such as the drag force experienced by a heavy quark plowing the plasma, the jet quenching parameter of the medium, the screening length between a quark-antiquark pair, and the production rate of thermal photons emitted by the plasma. We compare our results, when possible, with the corresponding weak-coupling results obtained with per- turbative techniques and with the experimental results from the heavy ion collision experiments at RHIC and LHC.

2013 - Quarkonium dissociation by anisotropy [Articolo su rivista]
Chernicoff, Mariano; Fernández, Daniel; Mateos, David; Trancanelli, Diego
abstract

We compute the screening length for quarkonium mesons moving through an anisotropic, strongly coupled N=4 super Yang-Mills plasma by means of its gravity dual. We present the results for arbitrary velocities and orientations of the mesons, as well as for arbitrary values of the anisotropy. The anisotropic screening length can be larger or smaller than the isotropic one, and this depends on whether the comparison is made at equal temperatures or at equal entropy densities. For generic motion we find that: (i) mesons dissociate above a certain critical value of the anisotropy, even at zero temperature; (ii) there is a limiting velocity for mesons in the plasma, even at zero temperature; (iii) in the ultra-relativistic limit the screening length scales as (1−v2)ϵ with epsilon =1/2, in contrast with the isotropic result epsilon =1/4.

2013 - Thermal photon production in a strongly coupled anisotropic plasma [Articolo su rivista]
Patiño, Leonardo; Trancanelli, Diego
abstract

Photons produced in heavy ion collisions escape virtually unperturbed from the surrounding medium, thus representing an excellent probe of the conditions at the emission point. Using the gauge/gravity duality, we calculate the rate of photon production in an anisotropic, strongly coupled N=4 plasma with Nf<

2012 - Drag force in a strongly coupled anisotropic plasma [Articolo su rivista]
Chernicoff, Mariano; Fernández, Daniel; Mateos, David; Trancanelli, Diego
abstract

We calculate the drag force experienced by an infinitely massive quark propagating at constant velocity through an anisotropic, strongly coupled N=4 plasma by means of its gravity dual. We find that the gluon cloud trailing behind the quark is generally misaligned with the quark velocity, and that the latter is also misaligned with the force. The drag coefficient μ can be larger or smaller than the corresponding isotropic value depending on the velocity and the direction of motion. In the ultra-relativistic limit we find that generically μ ∝ p. We discuss the conditions under which this behaviour may extend to more general situations.

2012 - Jet quenching in a strongly coupled anisotropic plasma [Articolo su rivista]
Chernicoff, Mariano; Fernández, Daniel; Mateos, David; Trancanelli, Diego
abstract

The jet quenching parameter of an anisotropic plasma depends on the relative orientation between the anisotropic direction, the direction of motion of the parton, and the direction along which the momentum broadening is measured. We calculate the jet quenching parameter of an anisotropic, strongly coupled N=4 plasma by means of its gravity dual. We present the results for arbitrary orientations and arbitrary values of the anisotropy. The anisotropic value can be larger or smaller than the isotropic one, and this depends on whether the comparison is made at equal temperatures or at equal entropy densities. We compare our results to analogous calculations for the real-world quark-gluon plasma and find agreement in some cases and disagreement in others.

2012 - Strong Coupling Isotropization of Non-Abelian Plasmas Simplified [Articolo su rivista]
Heller, Michal P.; Mateos, David; van der Schee, Wilke; Trancanelli, Diego
abstract

We study the isotropization of a homogeneous, strongly coupled, non-Abelian plasma by means of its gravity dual. We compare the time evolution of a large number of initially anisotropic states as determined, on the one hand, by the full non-linear Einstein's equations and, on the other, by the Einstein's equations linearized around the final equilibrium state. The linear approximation works remarkably well even for states that exhibit large anisotropies. For example, it predicts with a 20% accuracy the isotropization time, which is of the order of tiso ≲ 1/T, with T the final equilibrium temperature. We comment on possible extensions to less symmetric situations.

2011 - Anisotropic N=4 super Yang-Mills Plasma and Its Instabilities [Articolo su rivista]
Mateos, David; Trancanelli, Diego
abstract

We present a IIB supergravity solution dual to a spatially anisotropic finite-temperature N=4 super Yang-Mills plasma. The solution is static, possesses an anisotropic horizon, and is completely regular. The full geometry can be viewed as a renormalization group flow from an AdS geometry in the ultraviolet to a Lifshitz-like geometry in the infrared. The anisotropy can be equivalently understood as resulting from a position-dependent theta-term or from a non-zero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics of the system. We construct the phase diagram, which exhibits homogeneous and inhomogeneous (i.e. mixed) phases, and comment on similarities with QCD at finite baryon density. At low densities the homogeneous phase displays several instabilities reminiscent of instabilities of weakly coupled plasmas.

2011 - Dynamical tachyons on fuzzy spheres [Articolo su rivista]
Berenstein, David; Trancanelli, Diego
abstract

We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the BMN plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills on a sphere, of which this system is a truncation. We also set up a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.

2011 - Evidence for Fast Thermalization in the Plane-Wave Matrix Model [Articolo su rivista]
Asplund, Curtis T.; Berenstein, David; Trancanelli, Diego
abstract

We perform a numerical simulation of the classical evolution of the plane-wave matrix model with semiclassical initial conditions. Some of these initial conditions thermalize and are dual to a black hole forming from the collision of D-branes in the plane wave geometry. In particular, we consider a large fuzzy sphere (a D2-brane) plus a single eigenvalue (a D0-particle) going exactly through the center of the fuzzy sphere and aimed to intersect it. Including quantum fluctuations of the off-diagonal modes in the initial conditions, with sufficient kinetic energy the configuration collapses to a small size. We also find evidence for fast thermalization: rapidly decaying autocorrelation functions at late times with respect to the natural time scale of the system.

2011 - Thermodynamics and instabilities of a strongly coupled anisotropic plasma [Articolo su rivista]
Mateos, David; Trancanelli, Diego
abstract

We extend our analysis of a IIB supergravity solution dual to a spatially anisotropic finite-temperature N=4 super Yang-Mills plasma. The solution is static, possesses an anisotropic horizon, and is completely regular. The full geometry can be viewed as a renormalization group flow from an AdS geometry in the ultraviolet to a Lifshitz-like geometry in the infrared. The anisotropy can be equivalently understood as resulting from a position-dependent theta-term or from a non-zero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics. The phase diagram exhibits homogeneous and inhomogeneous (i.e. mixed) phases. In some regions the homogeneous phase displays instabilities reminiscent of those of weakly coupled plasmas. We comment on similarities with QCD at finite baryon density and with the phenomenon of cavitation.

2010 - A supermatrix model for N= 6 super Chern-Simons-matter theory [Articolo su rivista]
Drukker, Nadav; Trancanelli, Diego
abstract

We construct the Wilson loop operator of N=6 super Chern-Simons-matter which is invariant under half of the supercharges of the theory and is dual to the simplest macroscopic open string in AdS4×CP3. The Wilson loop couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bi-fundamental representation of the U(N)×U(M) gauge group. These ingredients are naturally combined into a superconnection whose holonomy gives the Wilson loop, which can be defined for any representation of the supergroup U(N|M). Explicit expressions for loops supported along an infinite straight line and along a circle are presented. Using the localization calculation of Kapustin et al. we show that the circular loop is computed by a supermatrix model and discuss the connection to pure Chern-Simons theory with supergroup U(N|M).

2009 - Emergent geometry in N=6 Chern-Simons-matter theory [Relazione in Atti di Convegno]
Trancanelli, Diego
abstract

We investigate a strong coupling expansion of N=6 superconformal Chern-Simons theory obtained from the semiclassical analysis of low energy, effective degrees of freedom given by the eigenvalues of a certain matrix model. We show how the orbifolded sphere S7/Zk of the dual geometry emerges dynamically from the distribution of the eigenvalues. As a test of this approach we compute the energy of off-diagonal excitations, finding perfect agreement with the dispersion relation of giant magnons.

2009 - Quantum 't Hooft operators and S-duality in N=4 super Yang-Mills [Articolo su rivista]
Gomis, Jaume; Okuda, Takuya; Trancanelli, Diego
abstract

We provide a quantum path integral definition of an 't Hooft loop operator, which inserts a pointlike monopole in a four dimensional gauge theory. We explicitly compute the expectation value of the circular 't Hooft operators in N=4 super Yang-Mills with arbitrary gauge group G up to next to leading order in perturbation theory. We also compute in the strong coupling expansion the expectation value of the circular Wilson loop operators. The result of the computation of an 't Hooft loop operator in the weak coupling expansion exactly reproduces the strong coupling result of the conjectured dual Wilson loop operator under the action of S-duality. This paper demonstrates - for the first time - that correlation functions in N=4 super Yang-Mills admit the action of S-duality.

2008 - Spectral curves, emergent geometry, and bubbling solutions for Wilson loops [Articolo su rivista]
Okuda, Takuya; Trancanelli, Diego
abstract

We study the supersymmetric circular Wilson loops of N=4 super Yang-Mills in large representations of the gauge group. In particular, we obtain the spectral curves of the matrix model which captures the expectation value of the loops. These spectral curves are then proven to be precisely the hyperelliptic surfaces that characterize the bubbling solutions dual to the Wilson loops, thus yielding an example of a geometry emerging from an eigenvalue distribution. We finally discuss the Wilson loop expectation value from the matrix model and from supergravity.

2008 - Supersymmetric Wilson loops on S^3 [Articolo su rivista]
Drukker, Nadav; Giombi, Simone; Ricci, Riccardo; Trancanelli, Diego
abstract

We compute the screening length for quarkonium mesons moving through an anisotropic, strongly coupled N=4 super Yang-Mills plasma by means of its gravity dual. We present the results for arbitrary velocities and orientations of the mesons, as well as for arbitrary values of the anisotropy. The anisotropic screening length can be larger or smaller than the isotropic one, and this depends on whether the comparison is made at equal temperatures or at equal entropy densities. For generic motion we find that: (i) mesons dissociate above a certain critical value of the anisotropy, even at zero temperature/ (ii) there is a limiting velocity for mesons in the plasma, even at zero temperature/ (iii) in the ultra-relativistic limit the screening length scales as (1-v2)ε with ε =1/2, in contrast with the isotropic result ε =1/4.

2008 - Three-dimensional N=6 superconformal field theories and their membrane dynamics [Articolo su rivista]
Berenstein, David; Trancanelli, Diego
abstract

We analyze several aspects of the recent construction of three-dimensional conformal gauge theories by Aharony et al. in various regimes. We pay special attention to understanding how the M-theory geometry and interpretation can be extracted from the analysis of the field theory. We revisit the calculations of the moduli space of vacua and the complete characterization of chiral ring operators by analyzing the field theory compactified on a 2-sphere. We show that many of the states dual to these operators can be interpreted as D-brane states in the weak coupling limit. Also, various features of the dual AdS geometry can be obtained by performing a strong coupling expansion around moduli space configurations, even though one is not taking the planar expansion. In particular, we show that at strong coupling the corresponding weak coupling D-brane states of the chiral ring localize on particular submanifolds of the dual geometry that match the M-theory interpretation. We also study the massive spectrum of fields in the moduli space. We use this to investigate the dispersion relation of giant magnons from the field theory point of view. Our analysis predicts the exact functional form of the dispersion relation as a function of the world-sheet momentum, independently of integrability assumptions, but not the exact form with respect to the 't Hooft coupling. We also get the dispersion relation of bound states of giant magnons from first principles, providing evidence for the full integrability of the corresponding spin chain model at strong 't Hooft coupling.

2008 - Wilson loop correlators at strong coupling: from matrices to bubbling geometries [Articolo su rivista]
Gomis, Jaume; Matsuura, Shunji; Okuda, Takuya; Trancanelli, Diego
abstract

We compute at strong coupling the large N correlation functions of supersymmetric Wilson loops in large representations of the gauge group with local operators of N=4 super Yang-Mills. The gauge theory computation of these correlators is performed using matrix model techniques. We show that the strong coupling correlator of the Wilson loop with the stress tensor computed using the matrix model exactly matches the semiclassical computation of the correlator of the 't Hooft loop with the stress tensor, providing a non-trivial quantitative test of electric-magnetic duality of N=4 super Yang-Mills. We then perform these calculations using the dual bulk gravitational picture, where the Wilson loop is described by a 'bubbling' geometry. By applying holographic methods to these backgrounds we calculate the Wilson loop correlation functions, finding perfect agreement with our gauge theory results.

2008 - Wilson loops: From 4D supersymmetric Yang-Mills theory to 2D Yang-Mills theory [Articolo su rivista]
Drukker, Nadav; Giombi, Simone; Ricci, Riccardo; Trancanelli, Diego
abstract

We present a large new family of Wilson loop operators in N=4 supersymmetric Yang-Mills theory. For an arbitrary curve on the three dimensional sphere one can add certain scalar couplings to the Wilson loop so it preserves at least two supercharges. Some previously known loops, notably the 1/2 BPS circle, belong to this class, but we point out many more special cases which were not known before and could provide further tests of the AdS/CFT correspondence.

2007 - Half-BPS geometries and thermodynamics of free fermions [Articolo su rivista]
Giombi, Simone; Kulaxizi, Manuela; Ricci, Riccardo; Trancanelli, Diego
abstract

Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the 'bubbling AdS' construction of Lin, Lunin and Maldacena. In this paper we study the half-BPS geometry associated with a gas of free fermions in thermodynamic equilibrium obeying the Fermi-Dirac distribution. We consider both regimes of low and high temperature. In the former case, we present a detailed computation of the ADM mass of the supergravity solution and find agreement with the thermal energy of the fermions. The solution has a naked null singularity and, by general arguments, is expected to develop a finite area horizon once stringy corrections are included. By introducing a stretched horizon, we propose a way to match the entropy of the fermions with the entropy of the geometry in the low temperature regime. In the opposite limit of high temperature, the solution resembles a dilute gas of D3 branes. Also in this case the ADM mass of the geometry agrees with the thermal energy of the fermions.

2007 - More supersymmetric Wilson loops [Articolo su rivista]
Drukker, Nadav; Giombi, Simone; Ricci, Riccardo; Trancanelli, Diego
abstract

We present a large new family of Wilson loop operators in N=4 supersymmetric Yang-Mills theory. For an arbitrary curve on the three dimensional sphere one can add certain scalar couplings to the Wilson loop so it preserves at least two supercharges. Some previously known loops, notably the 1/2 BPS circle, belong to this class, but we point out many more special cases which were not known before and could provide further tests of the AdS/CFT correspondence.

2007 - On the D3-brane description of some 1/4 BPS Wilson loops [Articolo su rivista]
Drukker, Nadav; Giombi, Simone; Ricci, Riccardo; Trancanelli, Diego
abstract

Recently it has been proposed that Wilson loops in high-dimensional representations in N=4 supersymmetric Yang-Mills theory (or multiply wrapped loops) are described by D-branes in AdS5×S5, rather than by fundamental strings. Thus far explicit D3-brane solutions have been only found in the case of the half-BPS circle or line. Here we present D3-brane solutions describing some 1/4 BPS loops. In one case, where the loop is conjectured to be given by a Gaussian matrix model, the action of the brane correctly reproduces the expectation value of the Wilson loop including all 1/N corrections at large λ. As in the corresponding string solution, here too we find two classical solutions, one stable and one not. The unstable one contributes exponentially small corrections that agree with the matrix model calculation.

2007 - Studies in gauge/string dualities [Monografia/Trattato scientifico]
Trancanelli, Diego
abstract

Dualities are among the most powerful tools in theoretical physics and, particularly, in string theory. The ones relating gauge field theories and theories of strings, the gauge/string dualities, are specially important and constitute the focus of this dissertation. We consider several topics in the context of two such dualities, the AdS/CFT correspondence and twistor string theory. In the part about the AdS/CFT correspondence we start by studying the thermodynamics of type IIB superstrings on the maximally supersymmetric plane wave background, computing in particular the Hagedorn temperature of non-interacting strings and analyzing the limits of small and large background Ramond-Ramond flux. We then consider a half-BPS supergravity solution whose moduli space can be mapped to the phase space of a gas of free fermions in a harmonic potential at finite temperature. We can match the ADM mass of the geometry with the thermal energy of the fermions and propose a way to also match the entropies in the two pictures. The last chapter of this part is dedicated to the study of supersymmetric Wilson loops. We first introduce a large new family of loop operators preserving various amounts of supersymmetry, from two to sixteen supercharges. We then study a novel description of higher rank loops in terms of electrically charged D-branes. In particular, we compute correlation functions between such loops and chiral primary operators of N = 4 super Yang-Mills theory and present the D-brane solutions corresponding to some examples of quarter-BPS loop operators. In the part about twistor string theory we first extend the conjectured equivalence between perturbative N = 4 super Yang-Mills and the topological B-model on CP3|4 to N = 1 and N = 2 superconformal quiver gauge theories. This is achieved by orbifolding the fermionic directions of the supertwistor space. We also consider some explicit quivers and compute several scattering amplitudes. Finally, we check the localization properties of some gravity amplitudes in twistor space and propose an extension of the twistor inspired MHV decomposition of Feynamn diagrams to the computation of tree level graviton scattering.

2006 - Operator product expansion of higher rank Wilson loops from D-branes and matrix models [Articolo su rivista]
Giombi, Simone; Ricci, Riccardo; Trancanelli, Diego
abstract

In this paper we study correlation functions of circular Wilson loops in higher dimensional representations with chiral primary operators of N=4 super Yang-Mills theory. This is done using the recently established relation between higher rank Wilson loops in gauge theory and D-branes with electric fluxes in supergravity. We verify our results with a matrix model computation, finding perfect agreement in both the symmetric and the antisymmetric case.

2005 - Instantons and matter in N = 1/2 supersymmetric gauge theory [Articolo su rivista]
Giombi, Simone; Ricci, Riccardo; Robles-Llana, Daniel; Trancanelli, Diego
abstract

We extend the instanton calculus for N=1/2 U(2) supersymmetric gauge theory by including one massless flavor. We write the equations of motion at leading order in the coupling constant and we solve them exactly in the non(anti)commutativity parameter C. The profile of the matter superfield is deformed through linear and quadratic corrections in C. Higher order corrections are absent because of the fermionic nature of the back-reaction. The instanton effective action, in addition to the usual 't Hooft term, includes a contribution of order C2 and is N=1/2 invariant. We argue that the N=1 result for the gluino condensate is not modified by the presence of the new term in the effective action.

2005 - Orbifolding the twistor string [Articolo su rivista]
Giombi, S.; Kulaxizi, M.; Ricci, R.; Robles-Llana, D.; Trancanelli, D.; Zoubos, K.
abstract

The D-instanton expansion of the topological B-model on the supermanifold CP(3|4) reproduces the perturbative expansion of N=4 Super Yang-Mills theory. In this paper we consider orbifolds in the fermionic directions of CP(3|4). This operation breaks the SU(4) R-symmetry group, reducing the amount of supersymmetry of the gauge theory. As specific examples we take N=1 and N=2 orbifolds and obtain the corresponding superconformal quiver theories. We discuss the D1 instanton expansion in this context and explicitly compute some amplitudes.

2004 - A Note on Twistor Gravity Amplitudes [Articolo su rivista]
Giombi, Simone; Ricci, Riccardo; Robles-Llana, Daniel; Trancanelli, Diego
abstract

In a recent paper, Witten proposed a surprising connection between perturbative gauge theory and a certain topological model in twistor space. In particular, he showed that gluon amplitudes are localized on holomorphic curves. In this note we present some preliminary considerations on the possibility of having a similar localization for gravity amplitudes.

2003 - The superstring Hagedorn temperature in a pp-wave background [Articolo su rivista]
Grignani, Gianluca; Orselli, Marta; Semenoff, Gordon W; Trancanelli, Diego
abstract

The thermodynamics of type IIB superstring theory in the maximally supersymmetric plane wave background is studied. We compute the thermodynamic partition function for non-interacting strings exactly and the result differs slightly from previous computations. We clarify some of the issues related to the Hagedorn temperature in the limits of small and large constant RR 5-form. We study the thermodynamic behavior of strings in the case of AdS3 × S3 × T4 geometries in the presence of NS-NS and RR 3-form backgrounds. We also comment on the relationship of string thermodynamics and the thermodynamic behavior of the sector of Yang-Mills theory which is the holographic dual of the string theory.