When mass-deformed ABJM theory is considered on S-3, the partition function of the theory localises, and is given by a matrix model. At large N, we solve this model in the decompactification limit, where the radius of the three-sphere is taken to infinity. In this limit, the theory exhibits a rich phase structure with an infinite number of third-order quantum phase transitions, accumulating at strong coupling.
We study local temperature fluctuations in a 2+1 dimensional CFT on the sphere, dual to a black hole in asymptotically AdS spacetime. The fluctuation spectrum is governed by the lowest-lying hydrodynamic modes of the system whose frequency and damping rate determine whether temperature fluctuations are thermal or quantum. We calculate numerically the corresponding quasinormal frequencies and match the result with the hydrodynamics of the dual CFT at high temperature. As a by-product of our analysis we determine the appropriate boundary conditions for calculating low-lying quasinormal modes for a four-dimensional Reissner-Nordstrom black hole in global AdS.
N - 2* gauge theory in four space-time dimensions arises as a deformation of the parent N = 4 supersymmetric Yang-Mills theory under which its hypermultiplet acquires a mass. This theory, on the one hand, has a known supergravity dual and on the other hand is amenable to localization. We explain, using localization, a dynamical selection of the supergravity Coulomb branch vacuum at large N. We also demonstrate that large Wilson loops obey perimeter law, again finding exact match between direct field-theory calculations and string theory. Additionally, we compute free energy at large 't Hooft coupling.
One-point functions of certain non-protected scalar operators in the defect CFT dual to the D3-D5 probe brane system with k units of world volume flux can be expressed as overlaps between Bethe eigenstates of the Heisenberg spin chain and a matrix product state. We present a closed expression of determinant form for these one-point functions, valid for any value of k. The determinant formula factorizes into the k = 2 result times a k-dependent pre-factor. Making use of the transfer matrix of the Heisenberg spin chain we recursively relate the matrix product state for higher even and odd k to the matrix product state for k = 2 and k = 3 respectively. We furthermore find evidence that the matrix product states for k = 2 and k = 3 are related via a ratio of Baxter's Q-operators. The general k formula has an interesting thermodynamical limit involving a non-trivial scaling of k, which indicates that the match between string and field theory one-point functions found for chiral primaries might be tested for non-protected operators as well. We revisit the string computation for chiral primaries and discuss how it can be extended to non-protected operators.
We study string quantum corrections to the ratio of latitude and circular Wilson loops in N = 4 super-Yang-Mills theory at strong coupling. Conformal gauge for the corresponding minimal surface in AdS(5) x S-5 is singular and we show that an IR anomaly associated with the divergence in the conformal factor removes previously reported discrepancy with the exact field -theory result. We also carefully check conformal anomaly cancellation and recalculate fluctuation determinants by directly evaluting phaseshifts for all the fluctuation modes.
We construct topological Wess-Zumino term for supercoset sigma-models on various AdS(3) backgrounds. For appropriately chosen set of parameters, the sigma-model remains integrable when the Wess-Zumino term is added to the action. Moreover, the conditions for integrability, kappa-symmetry and conformal invariance are equivalent to each other.
The planar N = 2* Super-Yang-Mills (SYM) theory is solved at large 't Hooft coupling using localization on S-4. The solution permits detailed investigation of the resonance phenomena responsible for quantum phase transitions in infinite volume, and leads to quantitative predictions for the semiclassical string dual of the N = 2* theory.
We construct the D3-brane solution in the holographic dual of the N = 2* theory that describes Wilson lines in symmetric representations of the gauge group. The results perfectly agree with the direct field-theory predictions based on localization.
By considering a Gaussian truncation of N = 4 super Yang-Mills, we derive a set of Dyson equations that account for the ladder diagram contribution to connected correlators of circular Wilson loops. We consider different numbers of loops, with different relative orientations. We show that the Dyson equations admit a spectral representation in terms of eigenfunctions of a Schrodinger problem, whose classical limit describes the strong coupling limit of the ladder resummation. We also verify that in supersymmetric cases the exact solution to the Dyson equations reproduces known matrix model results.
We calculate planar tree level one-point functions of non-protected operators in the defect conformal field theory dual to the D3-D5 brane system with k units of the world volume flux. Working in the operator basis of Bethe eigenstates of the Heisenberg XXX1/2 spin chain we express the one-point functions as overlaps of these eigenstates with a matrix product state. For k = 2 we obtain a closed expression of determinant form for any number of excitations, and in the case of half-filling we find a relation with the Neel state. In addition, we present a number of results for the limiting case k -> infinity.
Partial Neel states are generalizations of the ordinary Neel (classical anti-ferromagnet) state that can have arbitrary integer spin. We study overlaps of these states with Bethe states. We first identify this overlap with a partial version of reflecting-boundary domain-wall partition function, and then derive various determinant representations for off-shell and on-shell Bethe states.
We study the null dipole deformation of N = 4 super Yang-Mills theory, which is an example of a potentially solvable 'dipole CFT': a theory that is non-local along a null direction, has non-relativistic conformal invariance along the remaining ones, and is holographically dual to a Schrodinger space-time. We initiate the field-theoretical study of the spectrum in this model by using integrability inherited from the parent theory. The dipole deformation corresponds to a nondiagonal Drinfeld-Reshetikhin twist in the spin chain picture, which renders the traditional Bethe ansatz inapplicable from the very beginning. We use instead the Baxter equation supplemented with nontrivial asymptotics, which gives the full 1-loop spectrum in the sl(2) sector. We show that anomalous dimensions of long gauge theory operators perfectly match the string theory prediction, providing a quantitative test of Schrodinger holography.
We initiate a systematic, non-perturbative study of the large-N expansion in the two-dimensional SU(N) x SU(N) principal Chiral model (PCM). Starting with the known infinite-N solution for the ground state at fixed chemical potential, we devise an iterative procedure to solve the Bethe ansatz equations order by order in 1/N. The first few orders, which we explicitly compute, reveal a systematic enhancement pattern at strong coupling calling for the near-threshold resummation of the large-N expansion. The resulting double-scaling limit bears striking similarities to the c = 1 noncritical string theory and suggests that the double-scaled PCM is dual to a noncritical string with a (2 + 1)-dimensional target space where an additional dimension emerges dynamically from the SU(N) Dynkin diagram.
The encoding of all possible sets of Bethe equations for a spin chain with SU(N vertical bar M) symmetry into a QQ-system calls for an expression of spin chain overlaps entirely in terms of Q-functions. We take a significant step towards deriving such a universal formula in the case of overlaps between Bethe eigenstates and integrable boundary states, of relevance for AdS/dCFT, by determining the transformation properties of the overlaps under fermionic as well as bosonic dualities which allows us to move between any two descriptions of the spin chain encoded in the QQ-system. An important part of our analysis involves introducing a suitable regularization for singular Bethe root configurations.
A D3-D5 intersection gives rise to a defect CFT, wherein the rank of the gauge group jumps by k units across a domain wall. The one-point functions of local operators in this set-up map to overlaps between on-shell Bethe states in the underlying spin chain and a boundary state representing the D5 brane. Focussing on the k = 1 case, we extend the construction to gluonic and fermionic sectors, which was prohibitively difficult for k > 1. As a byproduct, we test an all-loop proposal for the one-point functions in the su(2) sector at the half-wrapping order of perturbation theory.
The psu(2, 2|4) integrable super spin chain underlying the AdS/CFT correspondence has integrable boundary states which describe set-ups where k D3-branes get dissolved in a probe D5-brane. Overlaps between Bethe eigenstates and these boundary states encode the one-point functions of conformal operators and are expressed in terms of the superdeterminant of the Gaudin matrix that in turn depends on the Dynkin diagram of the symmetry algebra. The different possible Dynkin diagrams of super Lie algebras are related via fermionic dualities and we determine how overlap formulae transform under these dualities. As an application we show how to consistently move between overlap formulae obtained for k = 1 from different Dynkin diagrams.
One-point functions of local operators are studied, at weak and strong coupling, for the ABJM theory in the presence of a 1/2 BPS domain wall. In the underlying quantum spin chain the domain wall is represented by a boundary state which we show is integrable yielding a compact determinant formula for one-point functions of generic operators.
The D3-D5 probe-brane system is holographically dual to a defect CFT which is known to be integrable. The evidence comes mainly from the study of correlation functions at weak coupling. In the present work we shed light on the emergence of integrability on the string theory side. We do so by constructing the double row transfer matrix which is conserved when the appropriate boundary conditions are imposed. The corresponding reflection matrix turns out to be dynamical and depends both on the spectral parameter and the string embedding coordinates.
Previous attempts to match the exact N = 4 super Yang-Mills expression for the expectation value of the 1/2-BPS circular Wilson loop with the semiclassical AdS(5) x S-5 string theory prediction were not successful at the first subleading order. There was a missing prefactor similar to lambda(-3/4) which could be attributed to the unknown normalization of the string path integral measure. Here we resolve this problem by computing the ratio of the string partition functions corresponding to the circular Wilson loop and the special 1/4-supersymmetric latitude Wilson loop. The fact that the latter has a trivial expectation value in the gauge theory allows us to relate the prefactor to the contribution of the three zero modes of the transverse fluctuation operator in the 5-sphere directions.
We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in N = 4 super Yang-Mills theory are invariant under a Yangian symmetry Y[psu(2, 2 vertical bar 4)] built upon the manifest superconformal symmetry algebra of the theory. The existence of this hidden symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the classical integrability of the dual AdS(5) x S-5 string description. The hidden symmetry generators consist of a canonical non-local second order variational derivative piece acting on the superpath, along with a novel local path dependent contribution. We match the functional form of these Yangian symmetry generators at weak and strong coupling and find evidence for an interpolating function. Our findings represent the smooth counterpart to the Yangian invariance of scattering superamplitudes dual to light-like polygonal super Wilson loops in the N = 4 super Yang-Mills theory.
Using exact results obtained from localization on S 4, we explore the large N limit of N = 2 super Yang-Mills theories with massive matter multiplets. We focus on three cases: N = 2* theory, describing a massive hypermultiplet in the adjoint representation, SU(N) super-Yang-Mills with 2 N massive hypermultiplets in the fundamental, and super QCD with massive quarks. When the radius of the four-sphere is sent to infinity the theories at hand are described by solvable matrix models, which exhibit a number of interesting phenomena including quantum phase transitions at finite 't Hooft coupling.
We clarify the relationship between probe analysis of the supergravity dual and the large-N solution of the localization matrix model for the planar N=2 super-Yang-Mills theory. A formalism inspired by supergravity allows us to systematically solve the matrix model at strong coupling. Quite surprisingly, we find that quantum phase transitions, known to occur in the N=2 theory, start to be visible at the third order of the strong-coupling expansion and thus constitute a perturbative phenomenon on the string worldsheet.
We solve, using localization, for the large-N master field of N = 2* super-Yang-Mills theory. From that we calculate expectation values of large Wilson loops and the free energy on the four-sphere. At weak coupling, these observables only receive non-perturbative contributions. The analytic solution holds for a finite range of the 't Hooft coupling and terminates at the point of a large-N phase transition. We find evidence that as the coupling is further increased the theory undergoes an infinite sequence of similar transitions that accumulate at infinity.
Large-N phase transitions occurring in massive N = 2 theories can be probed by Wilson loops in large antisymmetric representations. The logarithm of the Wilson loop is effectively described by the free energy of a Fermi distribution and exhibits second-order phase transitions (discontinuities in the second derivatives) as the size of representation varies. We illustrate the general features of antisymmetric Wilson loops on a number of examples where the phase transitions are known to occur: N = 2 SQCD with various mass arrangements and N = 2* theory. As a byproduct, we solve planar N = 2 SQCD with three independent mass parameters. This model has two effective mass scales and undergoes two phase transitions.
We consider level crossing in a matrix family H = H-0 + lambda V where H-0 is a fixed N x N matrix and V belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing points in the complex plane of lambda, for which we obtain a number of exact, asymptotic and approximate formulas.
The holographic dual of N = 2*, D = 4 supersymmetric Yang-Mills theory has many features common to 5d CFT. We interpret this as a manifestation of Eguchi-Kawai mechanism.
Relatively low crossover temperature suggests that chiral symmetry restoration in Quantum Chromodynamics may well be described within the low-energy effective theory. The shape of the pseudocritical line in the T-mu plane is estimated within this assumption. No critical endpoint is found for physical values of quark masses.
Electrons in graphene exhibit hydrodynamic behavior in a certain range of temperatures. We indicate that in this regime electric current can result in cooling of electron fluid due to the Joule-Thomson effect. Cooling occurs in the Fermi-liquid regime, while for the Dirac fluid the effect results in heating.
An interplay between localization and holography is reviewed with the emphasis on the AdS5/CFT4 correspondence.
The circular Wilson loop in the two-node quiver CFT is computed at large-N and strong 't Hooft coupling by solving the localization matrix model.
The N=2* theory (mass deformation of the N=4 super-Yang-Mills theory) undergoes an infinite number of quantum phase transitions in the large-N limit. The phase structure and critical behavior can be analyzed using supersymmetric localization, which reduces the problem to an effective matrix model. We study this model in the strong-coupling phase.