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S. Prem Kumar

Swansea University, Physics, Faculty Member

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Ph.D. 1998, Carnegie Mellon University, USA.
Post-doctoral positions: University of Washington, Seattle.
Cambridge University.
5-year STFC Advanced Fellowship
at Swansea University.

Faculty at Swansea U.: 2005 - present.

Research interests: String theory, AdS/CFT correspondence, Supersymmetric Yang-Mills theories, Black Holes.
Address: Department of Physics,
Swansea University
Swansea, SA2 8PP, UK.

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Papers by S. Prem Kumar

Local quenches and quantum chaos from higher spin perturbations

by S. Prem Kumar and Justin David

We study local quenches in 1+1 dimensional conformal field theories at large-c by operators carry... more We study local quenches in 1+1 dimensional conformal field theories at large-c by operators carrying higher spin charge. Viewing such states as solutions in Chern-Simons theory, representing infalling massive particles with spin-three charge in the BTZ background , we use the Wilson line prescription to compute the single-interval entanglement entropy (EE) and scrambling time following the quench. We find that the change in EE is finite (and real) only if the spin-three charge q is bounded by the energy of the perturbation E, as |q|/c < E 2 /c 2. We show that the Wilson line/EE correlator deep in the quenched regime and its expansion for small quench widths overlaps with the Regge limit for chaos of the out-of-time-ordered correlator. We further find that the scrambling time for the two-sided mutual information between two intervals in the thermofield double state increases with increasing spin-three charge, diverging when the bound is saturated. For larger values of the charge, the scrambling time is shorter than for pure gravity and controlled by the spin-three Lyapunov exponent 4π/β. In a CFT with higher spin chemical potential, dual to a higher spin black hole, we find that the chemical potential must be bounded to ensure that the mutual information is a concave function of time and entanglement speed is less than the speed of light. In this case, a quench with zero higher spin charge yields the same Lyapunov exponent as pure Einstein gravity.

Holographic flows and thermodynamics of Polyakov loop impurities

We study holographic probes dual to heavy quark impurities interpolating between fundamental and ... more We study holographic probes dual to heavy quark impurities interpolating between fundamental and symmetric/antisymmetric tensor representations in strongly coupled N = 4 supersymmetric gauge theory. These correspond to non-conformal D3-and D5-brane probe embeddings in AdS 5 × S 5 exhibiting flows on their world-volumes. By examining the asymptotic regimes of the embeddings and the one-point function of static fields sourced by the boundary impurity, we conclude that the D5-brane embedding describes the screening of fundamental quarks in the UV into an antisymmetric source in the IR, whilst the non-conformal, D3-brane solution interpolates between the symmetric representation in the UV and fundamental sources in the IR. The D5-brane embeddings exhibit nontrivial thermodynamics with multiple branches of solutions, whilst the thermal analogue of the interpolating D3-brane solution does not appear to exist.

Universal corrections to entanglement entropy of local quantum quenches

We study the time evolution of single interval Rényi and entanglement en-tropies following local ... more We study the time evolution of single interval Rényi and entanglement en-tropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Rényi and entanglement entropies at order 2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the 2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential µ. We calculate the time dependence of the order 2 correction to the entanglement entropy for small µ, and show that the contribution at order µ 2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.

Quasinormal modes and holographic correlators in a crunching AdS geometry

We calculate frequency space holographic correlators in an asymptotically AdS crunching backgroun... more We calculate frequency space holographic correlators in an asymptotically AdS crunching background, dual to a relevant deformation of the M2-brane CFT placed in de Sitter spacetime. For massless bulk scalars, exploiting the connection to a solvable super-symmetric quantum mechanical problem, we obtain the exact frequency space correlator for the dual operator in the deformed CFT. Controlling the shape of the crunching surface in the Penrose diagram by smoothly dialling the deformation from zero to infinity, we observe that in the large deformation limit the Penrose diagram becomes a 'square', and the exact holographic correlators display striking similarities to their counterparts in the BTZ black hole and its higher dimensional generalisations. We numerically determine quasinor-mal poles for relevant and irrelevant operators, and find an intricate pattern of these in the complex frequency plane. In the case of relevant operators, the deformation parameter has an infinite sequence of critical values, each one characterised by a pair of poles colliding and moving away from the imaginary frequency axis with increasing deformation. In the limit of infinite deformation all scalar operators have identical quasinormal spectra. We compare and contrast our strongly coupled de Sitter QFT results with strongly coupled thermal correlators from AdS black holes.

Probing crunching AdS cosmologies

Holographic gravity duals of deformations of CFTs formulated on de Sitter spacetime contain FRW g... more Holographic gravity duals of deformations of CFTs formulated on de Sitter spacetime contain FRW geometries behind a horizon, with cosmological big crunch sin-gularities. Using a specific analytically tractable solution within a particular single scalar truncation of N = 8 supergravity on AdS 4 , we first probe such crunching cosmologies with spacelike radial geodesics that compute spatially antipodal correlators of large dimension boundary operators. At late times, the geodesics lie on the FRW slice of maximal expansion behind the horizon. The late time two-point functions factorise, and when transformed to the Einstein static universe, they exhibit a temporal non-analyticity determined by the maximal value of the scale factorã max. Radial geodesics connecting antipodal points necessarily have de Sitter energy E ˜ a max , while geodesics with E > ˜ a max terminate at the crunch, the two categories of geodesics being separated by the maximal expansion slice. The spacelike crunch singularity is curved " outward " in the Penrose diagram for the deformed AdS backgrounds, and thus geodesic limits of the antipodal correlators do not directly probe the crunch. Beyond the geodesic limit, we point out that the scalar wave equation, analytically continued into the FRW patch, has a potential which is singular at the crunch along with complex WKB turning points in the vicinity of the FRW crunch. We then argue that the frequency space Green's function has a branch point determined byã max which corresponds to the lowest quasinormal frequency.

Partition function of N = 2 * SYM on a large four-sphere

We examine the partition function of N = 2 * supersymmetric SU(N) Yang-Mills theory on the four-s... more We examine the partition function of N = 2 * supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N , is computed by saddle-points lying on walls of marginal stability on the Coulomb branch of the theory on R 4. For N an even (odd) integer and θ YM = 0 (π), these include a point of maximal degeneration of the Donagi-Witten curve to a torus where BPS dyons with electric charge N 2 become massless. We argue that the dyon singularity is the lone saddle-point in the SU(2) theory, while for SU(N) with N > 2, we characterize potentially competing saddle-points by obtaining the relations between the Seiberg-Witten periods at such points. Using Nekrasov's instanton partition function, we solve for the maximally degenerate saddle-point and obtain its free energy as a function of g YM and N , and show that the results are " large-N exact ". In the large-N theory our results provide analytical expressions for the periods/eigenvalues at the maximally degenerate saddle-point, precisely matching previously known formulae following from the correspondence between N = 2 * theory and the elliptic Calogero-Moser integrable model. The maximally singular point ceases to be a saddle-point of the partition function above a critical value of the coupling, in agreement with the recent findings of Russo and Zarembo.

Emergent Lifshitz scaling from N=4 SYM with supersymmetric heavy-quark density

We consider supersymmetric configurations in Type IIB supergravity obtained by the beackreaction ... more We consider supersymmetric configurations in Type IIB supergravity obtained by the beackreaction of fundamental strings ending on a stack of D3-branes and smeared uniformly in the three spatial directions along the D3-branes. These automatically include a distribution of D5-brane baryon vertices necessary to soak up string charge. The backgrounds are static, preserving eight supersymmetries, an SO(5) global symmetry and symmetry under spatial translations and rotations. We obtain the most general BPS configurations consistent with the symmetries. We show that the solutions to the Type IIB field equations are completely specified by a single function (the dilaton) satisfying a Poisson-like equation in two dimensions. We further find that the equation admits a class of solutions displaying Lifshitz-like scaling with dynamical critical exponent z=7. The equations also admit an asymptotically AdS_5 x S^5 solution deformed by the presence of backreacted string sources that yield a uniform density of heavy quarks in N=4 SYM.

Conformal perturbation theory and higher spin entanglement entropy on the torus

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphi... more We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential \mu, the deformation is related at high temperatures to a higher spin black hole in hs[0] theory on AdS_3 spacetime. We calculate the order \mu^2 corrections to the single interval Renyi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order \mu^2 corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Renyi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Renyi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

A universal correction to higher spin entanglement entropy

We consider conformal field theories in 1+1 dimensions with W-algebra symmetries, deformed by a c... more We consider conformal field theories in 1+1 dimensions with W-algebra symmetries, deformed by a chemical potential µ for the spin-three current. We show that the order µ 2 correction to the Rényi and entanglement entropies of a single interval in the deformed theory, on the infinite spatial line and at finite temperature, is universal. The correction is completely determined by the operator product expansion of two spin-three currents, and by the expectation values of the stress tensor, its descendants and its composites, evaluated on the n-sheeted Riemann surface branched along the interval. This explains the recently found agreement of the order µ 2 correction across distinct free field CFTs and higher spin black hole solutions holographically dual to CFTs with W-symmetry.

Higher spin entanglement entropy from CFT

We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential ... more We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential µ for the spin-three current. For the CFT on the infinite spatial line, we calculate the finite temperature entanglement entropy of a single interval perturbatively to second order in µ in each of the theories. We find that the result in each case is given by the same non-trivial function of temperature and interval length. Remarkably, we further obtain the same formula using a recent Wilson line proposal for the holographic entanglement entropy, in holomorphically factorized form, associated to the spin-three black hole in SL(3, R) × SL(3, R) Chern-Simons theory. Our result suggests that the order µ 2 correction to the entanglement entropy may be universal for W-algebra CFTs with spin-three chemical potential, and constitutes a check of the holographic entanglement entropy proposal for higher spin theories of gravity in AdS 3 .

Supersymmetric Lifshitz-like backgrounds from N=4 SYM with heavy quark density

We examine a class of gravity backgrounds obtained by considering the backreaction of a spatially... more We examine a class of gravity backgrounds obtained by considering the backreaction of a spatially uniform density of mutually BPS Wilson lines or heavy quarks in N = 4 SUSY Yang-Mills theory. The configurations preserve eight supercharges and an SO(5) subgroup of the SO(6) R-symmetry. They are obtained by considering the 1 4 -BPS geometries associated to smeared string/D3-brane (F1-D3) intersections. We argue that for the (partially) localized intersection, the geometry exhibits a flow from AdS 5 × S 5 in the UV to a novel IR scaling solution displaying anisotropic Lifshitz-like scaling with dynamical critical exponent z = 7, hyperscaling violation and a logarithmic running dilaton. We also obtain a two-parameter family of smeared 1 4 -BPS solutions on the Coulomb branch of N = 4 SYM exhibiting Lifshitz scaling and hyperscaling violation. For a certain parametric range these yield IR geometries which are conformal to AdS 2 × R 3 , and which have been argued to be relevant for fermionic physics.

Asymptotic symmetries and thermodynamics of higher spin black holes in AdS3

We study black holes carrying higher spin charge in AdS 3 within the framework of SL(N, R) × SL(N... more We study black holes carrying higher spin charge in AdS 3 within the framework of SL(N, R) × SL(N, R) Chern-Simons theory. Focussing attention on the N = 4 case, we explicitly analyze the asymptotic symmetry algebra of black hole solutions with a chemical potential for spin-four charge. We demonstrate that the background describes an RG flow between an IR fixed point with W 4 symmetry and a UV fixed point with W-symmetry associated to a non-principal embedding of sl(2) in sl(4). Matching Chern-Simons equations with Ward identities of the deformed CFT, we show that the UV stress tensor is twisted by a certain U(1) current, and the flow is triggered by an operator with dimension 4/3 at the UV fixed point. We find independent confirmation of this picture via a consistent formulation of thermodynamics with respect to this UV fixed point. We further analyze the thermodynamics of multiple branches of black hole solutions for N = 4, 5 and find that the BTZ-branch, dominant at low temperatures, ceases to exist at higher temperatures following a merger with a thermodynamically unstable branch. We also point out an interesting connection between the RG flows and generalized KdV hierarchies.

Heavy quark density in N=4 SYM: from hedgehog to Lifshitz spacetimes

We study the effect of an O(N 2 ) density of heavy quarks in strongly coupled N = 4 SUSY Yang-Mil... more We study the effect of an O(N 2 ) density of heavy quarks in strongly coupled N = 4 SUSY Yang-Mills theory in the large N limit. This is achieved in the type IIB supergravity dual by introducing a uniformly smeared density of macroscopic string sources stretching to the boundary of AdS 5 × S 5 . The backreacted system exhibits a flow from an AdS 5 "hedgehog" geometry to a scaling Lifshitz-like solution Lif 5 ×S 5 with dynamical critical exponent z = 7, wherein the scaling symmetry is broken by a logarithmic running dilaton. We find an exact black brane solution within the scaling regime which describes the low temperature thermodynamics of the system.

Thermodynamics of higher spin black holes in 3D

We examine the thermodynamic properties of recently constructed black hole solutions in SL(3, R) ... more We examine the thermodynamic properties of recently constructed black hole solutions in SL(3, R) × SL(3, R) Chern-Simons theory in the presence of a chemical potential for spin-3 charge, which acts as an irrelevant deformation of the dual CFT with W 3 × W 3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS 3 backgrounds corresponding to two different CFTs. The dominant branch at low temperatures, connected to the BTZ black hole, merges smoothly with a thermodynamically unstable branch and disappears at higher temperatures. We confirm that the UV region of the flow satisfies the Ward identities of a CFT with W

Large rank Wilson loops in N=2 superconformal QCD at strong coupling

We compute the expectation values of circular Wilson loops in large representations at strong cou... more We compute the expectation values of circular Wilson loops in large representations at strong coupling, in the large-N limit of the N = 2 superconformal theory with SU(N) gauge group and 2N hypermultiplets. Employing Pestun's matrix integral, we focus attention on symmetric and antisymmetric representations with ranks of order N. We find that large rank antisymmetric loops are independent of the coupling at strong 't Hooft coupling while symmetric Wilson loops grow exponentially with it. Symmetric loops display a non-analyticity as a function of the rank, characterized by the splitting of a single matrix model eigenvalue from the continuum, bearing close resemblance to Bose-Einstein condensation in an ideal gas. We discuss implications of these for a putative large-N string dual. The method of calculation we adopt makes explicit the connection to Fermi and Bose gas descriptions and also suggests a tantalizing connection of the above system to a multichannel Kondo model.

Weak coupling large-N transitions at finite baryon density

We study thermodynamics of free SU(N) gauge theory with a large number of colours and flavours on... more We study thermodynamics of free SU(N) gauge theory with a large number of colours and flavours on a three-sphere, in the presence of a baryon number chemical potential. Reducing the system to a holomorphic large-N matrix integral, paying specific attention to theories with scalar flavours (squarks), we identify novel third-order deconfining phase transitions as a function of the chemical potential. These transitions in the complex large-N saddle point configurations are interpreted as "melting" of baryons into (s)quarks. They are triggered by the exponentially large (∼ e N ) degeneracy of light baryon-like states, which include ordinary baryons, adjoint-baryons and baryons made from different spherical harmonics of flavour fields on the three-sphere. The phase diagram of theories with scalar flavours terminates at a phase boundary where baryon number diverges, representing the onset of Bose condensation of squarks.

Spinning flavour branes and fermion pairing instabilities

We consider probe Dp-branes, p = 3, 5, 7, in global AdS 5 × S 5 , rotating along an internal dire... more We consider probe Dp-branes, p = 3, 5, 7, in global AdS 5 × S 5 , rotating along an internal direction in the S 5 . These are dual to strongly interacting N = 4 SYM on S 3 with massless fundamental flavours, in the presence of an R-symmetry chemical potential for flavour fermions. For massless, "AdS-filling" Dp-brane embeddings at zero temperature, we find an infinite set of threshold values of the chemical potential at which instabilities are triggered. The onset of instability is always preceded by metastability of the zero density state. From the onset values of the chemical potential, we infer that unstable directions favour a homogeneous condensate of a bilinear made from fermion harmonics, or Cooper pairing. We confirm this picture both numerically and analytically. The linearized analysis showing the appearance of instabilities involves a charged scalar in global AdS space coupled to a (large) constant background gauge potential. The resulting frequency space correlator of the fermion bilinear at strong coupling displays poles in the upper half plane. In contrast, the correlator at zero coupling exhibits Pauli blocking due to occupation of states below the Fermi level, but no instabilities. The end-point of the strong coupling instability is not visible in our setup.

Towards holographic walking from N=4 super Yang-Mills

We propose that a holographic description of 'walking' behaviour, namely quasi-conformal dynamics... more We propose that a holographic description of 'walking' behaviour, namely quasi-conformal dynamics relevant for technicolor models, can be obtained from relevant deformations of N = 4 super Yang-Mills. We consider deformations which drive the theory close to the N = 1 Leigh-Strassler fixed point, eventually deviating from it in the deep IR. We use the Pilch-Warner dual supergravity description of the flow between the N = 4 and the N = 1 fixed points to focus on observables that only require knowledge of the walking region. These include large anomalous dimensions of quark bilinear operators, which we study via probe D7-branes. We also make a first attempt at describing the theory beyond the walking region by introducing an infrared cut-off, in the spirit of hard-wall models. In this case we find a light, dilaton-like scalar state, but whether this mode persists in the exact theory remains an open question.

Holographic Roberge-Weiss Transitions

We investigate N = 4 SYM coupled to fundamental flavours at nonzero imaginary quark chemical pote... more We investigate N = 4 SYM coupled to fundamental flavours at nonzero imaginary quark chemical potential in the strong coupling and large N limit, using gauge/gravity duality applied to the D3-D7 system, treating flavours in the probe approximation. The interplay between Z N symmetry and the imaginary chemical potential yields a series of first-order Roberge-Weiss transitions. An additional thermal transition separates phases where quarks are bound/unbound into mesons. This results in a set of Roberge-Weiss endpoints: we establish that these are triple points, determine the Roberge-Weiss temperature, give the curvature of the phase boundaries and confirm that the theory is analytic in µ 2 when µ 2 ≈ 0.

Quantum Phases of a Vortex String

We argue that the world-sheet dynamics of magnetic k-strings in the Higgs phase of the massdeform... more We argue that the world-sheet dynamics of magnetic k-strings in the Higgs phase of the massdeformed N = 4 theory, is controlled by a bosonic O(3) sigma model with anisotropy and a topological θ term. The theory interpolates between a massless O(2) symmetric regime, a massive O(3) symmetric phase and another massive phase with a spontaneously broken Z2 symmetry. The first two phases are separated by a Kosterlitz-Thouless transition. When θ = π, the O(3) symmetric phase flows to an interacting fixed point; sigma model kinks and their dyonic partners become degenerate, mirroring the behaviour of monopoles in the parent gauge theory. This leads to the identification of the kinks with monopoles confined on the string.

Local quenches and quantum chaos from higher spin perturbations

by S. Prem Kumar and Justin David

We study local quenches in 1+1 dimensional conformal field theories at large-c by operators carry... more We study local quenches in 1+1 dimensional conformal field theories at large-c by operators carrying higher spin charge. Viewing such states as solutions in Chern-Simons theory, representing infalling massive particles with spin-three charge in the BTZ background , we use the Wilson line prescription to compute the single-interval entanglement entropy (EE) and scrambling time following the quench. We find that the change in EE is finite (and real) only if the spin-three charge q is bounded by the energy of the perturbation E, as |q|/c < E 2 /c 2. We show that the Wilson line/EE correlator deep in the quenched regime and its expansion for small quench widths overlaps with the Regge limit for chaos of the out-of-time-ordered correlator. We further find that the scrambling time for the two-sided mutual information between two intervals in the thermofield double state increases with increasing spin-three charge, diverging when the bound is saturated. For larger values of the charge, the scrambling time is shorter than for pure gravity and controlled by the spin-three Lyapunov exponent 4π/β. In a CFT with higher spin chemical potential, dual to a higher spin black hole, we find that the chemical potential must be bounded to ensure that the mutual information is a concave function of time and entanglement speed is less than the speed of light. In this case, a quench with zero higher spin charge yields the same Lyapunov exponent as pure Einstein gravity.

Holographic flows and thermodynamics of Polyakov loop impurities

We study holographic probes dual to heavy quark impurities interpolating between fundamental and ... more We study holographic probes dual to heavy quark impurities interpolating between fundamental and symmetric/antisymmetric tensor representations in strongly coupled N = 4 supersymmetric gauge theory. These correspond to non-conformal D3-and D5-brane probe embeddings in AdS 5 × S 5 exhibiting flows on their world-volumes. By examining the asymptotic regimes of the embeddings and the one-point function of static fields sourced by the boundary impurity, we conclude that the D5-brane embedding describes the screening of fundamental quarks in the UV into an antisymmetric source in the IR, whilst the non-conformal, D3-brane solution interpolates between the symmetric representation in the UV and fundamental sources in the IR. The D5-brane embeddings exhibit nontrivial thermodynamics with multiple branches of solutions, whilst the thermal analogue of the interpolating D3-brane solution does not appear to exist.

Universal corrections to entanglement entropy of local quantum quenches

We study the time evolution of single interval Rényi and entanglement en-tropies following local ... more We study the time evolution of single interval Rényi and entanglement en-tropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Rényi and entanglement entropies at order 2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the 2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential µ. We calculate the time dependence of the order 2 correction to the entanglement entropy for small µ, and show that the contribution at order µ 2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.

Quasinormal modes and holographic correlators in a crunching AdS geometry

We calculate frequency space holographic correlators in an asymptotically AdS crunching backgroun... more We calculate frequency space holographic correlators in an asymptotically AdS crunching background, dual to a relevant deformation of the M2-brane CFT placed in de Sitter spacetime. For massless bulk scalars, exploiting the connection to a solvable super-symmetric quantum mechanical problem, we obtain the exact frequency space correlator for the dual operator in the deformed CFT. Controlling the shape of the crunching surface in the Penrose diagram by smoothly dialling the deformation from zero to infinity, we observe that in the large deformation limit the Penrose diagram becomes a 'square', and the exact holographic correlators display striking similarities to their counterparts in the BTZ black hole and its higher dimensional generalisations. We numerically determine quasinor-mal poles for relevant and irrelevant operators, and find an intricate pattern of these in the complex frequency plane. In the case of relevant operators, the deformation parameter has an infinite sequence of critical values, each one characterised by a pair of poles colliding and moving away from the imaginary frequency axis with increasing deformation. In the limit of infinite deformation all scalar operators have identical quasinormal spectra. We compare and contrast our strongly coupled de Sitter QFT results with strongly coupled thermal correlators from AdS black holes.

Probing crunching AdS cosmologies

Holographic gravity duals of deformations of CFTs formulated on de Sitter spacetime contain FRW g... more Holographic gravity duals of deformations of CFTs formulated on de Sitter spacetime contain FRW geometries behind a horizon, with cosmological big crunch sin-gularities. Using a specific analytically tractable solution within a particular single scalar truncation of N = 8 supergravity on AdS 4 , we first probe such crunching cosmologies with spacelike radial geodesics that compute spatially antipodal correlators of large dimension boundary operators. At late times, the geodesics lie on the FRW slice of maximal expansion behind the horizon. The late time two-point functions factorise, and when transformed to the Einstein static universe, they exhibit a temporal non-analyticity determined by the maximal value of the scale factorã max. Radial geodesics connecting antipodal points necessarily have de Sitter energy E ˜ a max , while geodesics with E > ˜ a max terminate at the crunch, the two categories of geodesics being separated by the maximal expansion slice. The spacelike crunch singularity is curved " outward " in the Penrose diagram for the deformed AdS backgrounds, and thus geodesic limits of the antipodal correlators do not directly probe the crunch. Beyond the geodesic limit, we point out that the scalar wave equation, analytically continued into the FRW patch, has a potential which is singular at the crunch along with complex WKB turning points in the vicinity of the FRW crunch. We then argue that the frequency space Green's function has a branch point determined byã max which corresponds to the lowest quasinormal frequency.

Partition function of N = 2 * SYM on a large four-sphere

We examine the partition function of N = 2 * supersymmetric SU(N) Yang-Mills theory on the four-s... more We examine the partition function of N = 2 * supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N , is computed by saddle-points lying on walls of marginal stability on the Coulomb branch of the theory on R 4. For N an even (odd) integer and θ YM = 0 (π), these include a point of maximal degeneration of the Donagi-Witten curve to a torus where BPS dyons with electric charge N 2 become massless. We argue that the dyon singularity is the lone saddle-point in the SU(2) theory, while for SU(N) with N > 2, we characterize potentially competing saddle-points by obtaining the relations between the Seiberg-Witten periods at such points. Using Nekrasov's instanton partition function, we solve for the maximally degenerate saddle-point and obtain its free energy as a function of g YM and N , and show that the results are " large-N exact ". In the large-N theory our results provide analytical expressions for the periods/eigenvalues at the maximally degenerate saddle-point, precisely matching previously known formulae following from the correspondence between N = 2 * theory and the elliptic Calogero-Moser integrable model. The maximally singular point ceases to be a saddle-point of the partition function above a critical value of the coupling, in agreement with the recent findings of Russo and Zarembo.

Emergent Lifshitz scaling from N=4 SYM with supersymmetric heavy-quark density

We consider supersymmetric configurations in Type IIB supergravity obtained by the beackreaction ... more We consider supersymmetric configurations in Type IIB supergravity obtained by the beackreaction of fundamental strings ending on a stack of D3-branes and smeared uniformly in the three spatial directions along the D3-branes. These automatically include a distribution of D5-brane baryon vertices necessary to soak up string charge. The backgrounds are static, preserving eight supersymmetries, an SO(5) global symmetry and symmetry under spatial translations and rotations. We obtain the most general BPS configurations consistent with the symmetries. We show that the solutions to the Type IIB field equations are completely specified by a single function (the dilaton) satisfying a Poisson-like equation in two dimensions. We further find that the equation admits a class of solutions displaying Lifshitz-like scaling with dynamical critical exponent z=7. The equations also admit an asymptotically AdS_5 x S^5 solution deformed by the presence of backreacted string sources that yield a uniform density of heavy quarks in N=4 SYM.

Conformal perturbation theory and higher spin entanglement entropy on the torus

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphi... more We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential \mu, the deformation is related at high temperatures to a higher spin black hole in hs[0] theory on AdS_3 spacetime. We calculate the order \mu^2 corrections to the single interval Renyi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order \mu^2 corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Renyi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Renyi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

A universal correction to higher spin entanglement entropy

We consider conformal field theories in 1+1 dimensions with W-algebra symmetries, deformed by a c... more We consider conformal field theories in 1+1 dimensions with W-algebra symmetries, deformed by a chemical potential µ for the spin-three current. We show that the order µ 2 correction to the Rényi and entanglement entropies of a single interval in the deformed theory, on the infinite spatial line and at finite temperature, is universal. The correction is completely determined by the operator product expansion of two spin-three currents, and by the expectation values of the stress tensor, its descendants and its composites, evaluated on the n-sheeted Riemann surface branched along the interval. This explains the recently found agreement of the order µ 2 correction across distinct free field CFTs and higher spin black hole solutions holographically dual to CFTs with W-symmetry.

Higher spin entanglement entropy from CFT

We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential ... more We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential µ for the spin-three current. For the CFT on the infinite spatial line, we calculate the finite temperature entanglement entropy of a single interval perturbatively to second order in µ in each of the theories. We find that the result in each case is given by the same non-trivial function of temperature and interval length. Remarkably, we further obtain the same formula using a recent Wilson line proposal for the holographic entanglement entropy, in holomorphically factorized form, associated to the spin-three black hole in SL(3, R) × SL(3, R) Chern-Simons theory. Our result suggests that the order µ 2 correction to the entanglement entropy may be universal for W-algebra CFTs with spin-three chemical potential, and constitutes a check of the holographic entanglement entropy proposal for higher spin theories of gravity in AdS 3 .

Supersymmetric Lifshitz-like backgrounds from N=4 SYM with heavy quark density

We examine a class of gravity backgrounds obtained by considering the backreaction of a spatially... more We examine a class of gravity backgrounds obtained by considering the backreaction of a spatially uniform density of mutually BPS Wilson lines or heavy quarks in N = 4 SUSY Yang-Mills theory. The configurations preserve eight supercharges and an SO(5) subgroup of the SO(6) R-symmetry. They are obtained by considering the 1 4 -BPS geometries associated to smeared string/D3-brane (F1-D3) intersections. We argue that for the (partially) localized intersection, the geometry exhibits a flow from AdS 5 × S 5 in the UV to a novel IR scaling solution displaying anisotropic Lifshitz-like scaling with dynamical critical exponent z = 7, hyperscaling violation and a logarithmic running dilaton. We also obtain a two-parameter family of smeared 1 4 -BPS solutions on the Coulomb branch of N = 4 SYM exhibiting Lifshitz scaling and hyperscaling violation. For a certain parametric range these yield IR geometries which are conformal to AdS 2 × R 3 , and which have been argued to be relevant for fermionic physics.

Asymptotic symmetries and thermodynamics of higher spin black holes in AdS3

We study black holes carrying higher spin charge in AdS 3 within the framework of SL(N, R) × SL(N... more We study black holes carrying higher spin charge in AdS 3 within the framework of SL(N, R) × SL(N, R) Chern-Simons theory. Focussing attention on the N = 4 case, we explicitly analyze the asymptotic symmetry algebra of black hole solutions with a chemical potential for spin-four charge. We demonstrate that the background describes an RG flow between an IR fixed point with W 4 symmetry and a UV fixed point with W-symmetry associated to a non-principal embedding of sl(2) in sl(4). Matching Chern-Simons equations with Ward identities of the deformed CFT, we show that the UV stress tensor is twisted by a certain U(1) current, and the flow is triggered by an operator with dimension 4/3 at the UV fixed point. We find independent confirmation of this picture via a consistent formulation of thermodynamics with respect to this UV fixed point. We further analyze the thermodynamics of multiple branches of black hole solutions for N = 4, 5 and find that the BTZ-branch, dominant at low temperatures, ceases to exist at higher temperatures following a merger with a thermodynamically unstable branch. We also point out an interesting connection between the RG flows and generalized KdV hierarchies.

Heavy quark density in N=4 SYM: from hedgehog to Lifshitz spacetimes

We study the effect of an O(N 2 ) density of heavy quarks in strongly coupled N = 4 SUSY Yang-Mil... more We study the effect of an O(N 2 ) density of heavy quarks in strongly coupled N = 4 SUSY Yang-Mills theory in the large N limit. This is achieved in the type IIB supergravity dual by introducing a uniformly smeared density of macroscopic string sources stretching to the boundary of AdS 5 × S 5 . The backreacted system exhibits a flow from an AdS 5 "hedgehog" geometry to a scaling Lifshitz-like solution Lif 5 ×S 5 with dynamical critical exponent z = 7, wherein the scaling symmetry is broken by a logarithmic running dilaton. We find an exact black brane solution within the scaling regime which describes the low temperature thermodynamics of the system.

Thermodynamics of higher spin black holes in 3D

We examine the thermodynamic properties of recently constructed black hole solutions in SL(3, R) ... more We examine the thermodynamic properties of recently constructed black hole solutions in SL(3, R) × SL(3, R) Chern-Simons theory in the presence of a chemical potential for spin-3 charge, which acts as an irrelevant deformation of the dual CFT with W 3 × W 3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS 3 backgrounds corresponding to two different CFTs. The dominant branch at low temperatures, connected to the BTZ black hole, merges smoothly with a thermodynamically unstable branch and disappears at higher temperatures. We confirm that the UV region of the flow satisfies the Ward identities of a CFT with W

Large rank Wilson loops in N=2 superconformal QCD at strong coupling

We compute the expectation values of circular Wilson loops in large representations at strong cou... more We compute the expectation values of circular Wilson loops in large representations at strong coupling, in the large-N limit of the N = 2 superconformal theory with SU(N) gauge group and 2N hypermultiplets. Employing Pestun's matrix integral, we focus attention on symmetric and antisymmetric representations with ranks of order N. We find that large rank antisymmetric loops are independent of the coupling at strong 't Hooft coupling while symmetric Wilson loops grow exponentially with it. Symmetric loops display a non-analyticity as a function of the rank, characterized by the splitting of a single matrix model eigenvalue from the continuum, bearing close resemblance to Bose-Einstein condensation in an ideal gas. We discuss implications of these for a putative large-N string dual. The method of calculation we adopt makes explicit the connection to Fermi and Bose gas descriptions and also suggests a tantalizing connection of the above system to a multichannel Kondo model.

Weak coupling large-N transitions at finite baryon density

We study thermodynamics of free SU(N) gauge theory with a large number of colours and flavours on... more We study thermodynamics of free SU(N) gauge theory with a large number of colours and flavours on a three-sphere, in the presence of a baryon number chemical potential. Reducing the system to a holomorphic large-N matrix integral, paying specific attention to theories with scalar flavours (squarks), we identify novel third-order deconfining phase transitions as a function of the chemical potential. These transitions in the complex large-N saddle point configurations are interpreted as "melting" of baryons into (s)quarks. They are triggered by the exponentially large (∼ e N ) degeneracy of light baryon-like states, which include ordinary baryons, adjoint-baryons and baryons made from different spherical harmonics of flavour fields on the three-sphere. The phase diagram of theories with scalar flavours terminates at a phase boundary where baryon number diverges, representing the onset of Bose condensation of squarks.

Spinning flavour branes and fermion pairing instabilities

We consider probe Dp-branes, p = 3, 5, 7, in global AdS 5 × S 5 , rotating along an internal dire... more We consider probe Dp-branes, p = 3, 5, 7, in global AdS 5 × S 5 , rotating along an internal direction in the S 5 . These are dual to strongly interacting N = 4 SYM on S 3 with massless fundamental flavours, in the presence of an R-symmetry chemical potential for flavour fermions. For massless, "AdS-filling" Dp-brane embeddings at zero temperature, we find an infinite set of threshold values of the chemical potential at which instabilities are triggered. The onset of instability is always preceded by metastability of the zero density state. From the onset values of the chemical potential, we infer that unstable directions favour a homogeneous condensate of a bilinear made from fermion harmonics, or Cooper pairing. We confirm this picture both numerically and analytically. The linearized analysis showing the appearance of instabilities involves a charged scalar in global AdS space coupled to a (large) constant background gauge potential. The resulting frequency space correlator of the fermion bilinear at strong coupling displays poles in the upper half plane. In contrast, the correlator at zero coupling exhibits Pauli blocking due to occupation of states below the Fermi level, but no instabilities. The end-point of the strong coupling instability is not visible in our setup.

Towards holographic walking from N=4 super Yang-Mills

We propose that a holographic description of 'walking' behaviour, namely quasi-conformal dynamics... more We propose that a holographic description of 'walking' behaviour, namely quasi-conformal dynamics relevant for technicolor models, can be obtained from relevant deformations of N = 4 super Yang-Mills. We consider deformations which drive the theory close to the N = 1 Leigh-Strassler fixed point, eventually deviating from it in the deep IR. We use the Pilch-Warner dual supergravity description of the flow between the N = 4 and the N = 1 fixed points to focus on observables that only require knowledge of the walking region. These include large anomalous dimensions of quark bilinear operators, which we study via probe D7-branes. We also make a first attempt at describing the theory beyond the walking region by introducing an infrared cut-off, in the spirit of hard-wall models. In this case we find a light, dilaton-like scalar state, but whether this mode persists in the exact theory remains an open question.

Holographic Roberge-Weiss Transitions

We investigate N = 4 SYM coupled to fundamental flavours at nonzero imaginary quark chemical pote... more We investigate N = 4 SYM coupled to fundamental flavours at nonzero imaginary quark chemical potential in the strong coupling and large N limit, using gauge/gravity duality applied to the D3-D7 system, treating flavours in the probe approximation. The interplay between Z N symmetry and the imaginary chemical potential yields a series of first-order Roberge-Weiss transitions. An additional thermal transition separates phases where quarks are bound/unbound into mesons. This results in a set of Roberge-Weiss endpoints: we establish that these are triple points, determine the Roberge-Weiss temperature, give the curvature of the phase boundaries and confirm that the theory is analytic in µ 2 when µ 2 ≈ 0.

Quantum Phases of a Vortex String

We argue that the world-sheet dynamics of magnetic k-strings in the Higgs phase of the massdeform... more We argue that the world-sheet dynamics of magnetic k-strings in the Higgs phase of the massdeformed N = 4 theory, is controlled by a bosonic O(3) sigma model with anisotropy and a topological θ term. The theory interpolates between a massless O(2) symmetric regime, a massive O(3) symmetric phase and another massive phase with a spontaneously broken Z2 symmetry. The first two phases are separated by a Kosterlitz-Thouless transition. When θ = π, the O(3) symmetric phase flows to an interacting fixed point; sigma model kinks and their dyonic partners become degenerate, mirroring the behaviour of monopoles in the parent gauge theory. This leads to the identification of the kinks with monopoles confined on the string.