arXiv subjects

S. Prem Kumar

Publications and source records attributed to S. Prem Kumar.

At least 19 recordsLinked to original sources

arXiv2026

Evaporating Black Hole Interior and Complexity Evolution

We study the evolution of the interior of an evaporating black hole in a simple model of Jackiw-Teitelboim (JT) gravity with an end-of-the-world (EoW) brane, where evaporation is modeled by entangling the brane's internal states with an auxiliary radiation system. To probe the black hole interior, we consider a geodesic length extracted from a boundary-to-brane two-point function and interpret its renormalised value as a measure of subsystem complexity. Our computation, based on quenched disorder averaging, includes non-perturbative gravitational effects from both spacetime wormholes and replica wormholes, encoding ensemble averaging over the dual random Hamiltonian and brane-state couplings. Unlike non-evaporating black holes, for which complexity first grows linearly and then plateaus at late times $\sim{\cal O}(e^{S_{\rm BH}})$, we find that complexity evolution of the black hole subsystem in the evaporating case differs drastically, depending nontrivially on the dimension of the emitted radiation Hilbert space. It grows linearly at early times, reaches a maximum shortly before the Page-time crossover $\sim{\cal O}({S_{\rm BH}})$, and then decays exponentially. We further show that the relative fluctuations of the interior length remain small before the Page time but become of order one and eventually large at later times: this signals a loss of self-averaging, with the ensemble-averaged complexity dominated by rare configurations rather than by typical realisations.

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arXiv2026

Entanglement Revivals and Scrambling for Evaporating Black Holes

We investigate the spreading of entanglement, and entanglement memory effects, in two-dimensional conformal field theory (CFT) propagating on evaporating black hole backgrounds. Memory effects leading to late-time spikes in mutual information for widely separated intervals are well known in CFTs admitting a quasiparticle description. In this work we examine the effect of black hole scrambling on late time mutual information spikes for disjoint intervals in free fermion CFT prepared in a thermofield double state. Late-time entanglement revival is driven by island-induced purification of modes in the union of the intervals. We show across two distinct 2d gravity models, Jackiw-Teitelboim (JT) gravity and the Russo-Susskind-Thorlacius (RST) model, that parametrically dialing up black hole scrambling time smooths out and suppresses entanglement spikes until they disappear at a critical scale, interpolating between free quasiparticle and maximal scrambling pictures. At the critical point, the interval lengths are exponential in black hole scrambling time. We further find a very closely related effect manifest as an entanglement dip for a single interval in a single-sided evaporating RST black hole.

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arXiv2025

Probing Evaporating Black Holes with Modular Flow in SYK

We study the effect of modular flow on correlation functions of fermions in the Sachdev-Ye-Kitaev (SYK) model coupled weakly to a bath, which we take to be another SYK model. The system and bath, together are prepared in the thermofield double (TFD) state, and we focus on the effect of modular flow generated by the reduced density matrix for the SYK system, obtained by tracing out the bath. We show, in the late time limit, that modular flowed correlators of two Majorana fermions, single-sided and two-sided, exhibit non-trivial singularities. Beyond a critical value of the modular parameter, the ``modular scrambling time", the singularity structure shows correlations being transferred from one boundary to the other. The calculations are performed by employing the replica trick in Euclidean time and appropriately analytically continuing to real time. Exploiting the connection between modular flow generators and SL$(2,{\mathbb R})$ boosts we use the microscopic picture to reconstruct the dual bulk modular flow in two-sided AdS$_2$ black hole spacetime. Fixed points of the flow allow to identify quantum extremal surfaces (QES) demarcating the entanglement wedge of the boundary system and the island. We show that bulk modular flow can move fermion insertions near the right boundary past the horizon leading to lightcone singularities in appropriately smeared boundary correlators, probing physics beyond the horizon.

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arXiv2024

Projections and teleportation of operator quenches in CFT

Motivated by recent proposals for information recovery from black holes via non-isometric maps and post-selection in an effective description, we set up and investigate a teleportation scenario in a 2d CFT involving a local operator quench and projection on a portion of space onto a Cardy state with the theory in the vacuum state. Using conformal invariance the system can be mapped to CFT with boundary (BCFT). Renyi entropies for spatial intervals in the projected state can then be computed as a function of the location of the quench, either using the replica method, or using twist fields, the latter employing universal results for correlators at large c. We find qualitatively distinct behaviours in the two systems. Our replica computations reveal a surprising universal n dependence of Renyi entropies which implies that teleportation does occur but is not optimal as would be expected because the projector is not especially tuned. We also find that the curious n dependence of the Renyi entropies means that the limit to the von Neumann entropy is not straightforward.

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arXiv2024

Replica R\'enyi Wormholes and Generalised Modular Entropy in JT Gravity

We consider the problem of computing semi-classical R\'enyi entropies of CFT on AdS$_2$ backgrounds in JT gravity with nongravitating baths, for general replica number $n$. Away from the $n\to 1$ limit, the backreaction of the CFT twist fields on the geometry is nontrivial. For one twist field insertion and general $n$, we show that the quantum extremal surface (QES) condition involves extremisation of the generalised modular entropy, consistent with Dong's generalisation of the Ryu-Takayanagi formula for general $n$. For multiple QES we describe replica wormhole geometries using the theory of Fuchsian uniformisation, explicitly working out the analytically tractable case of the $n=2$ double trumpet wormhole geometry. We determine the off-shell dependence of the gravitational action on the QES locations and boundary map. In a factorisation limit, corresponding to late times, we are able to relate this action functional to area terms given by the value of the JT dilaton at the (off-shell) QES locations, with computable corrections. Applied to the two-sided eternal black hole, we find the $n$-dependent Page times for R\'enyi enropies in the high temperature limit.

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arXiv2024

Twisted circle compactification of $\mathcal{N}=4$ SYM and its Holographic Dual

We consider a compactification of 4D $\mathcal{N}=4$ SYM, with $SU(N)$ gauge group, on a circle with anti-periodic boundary conditions for the fermions. We couple the theory to a constant background gauge field along the circle for an abelian subgroup of the $R$-symmetry which allows to preserve four supersymmetries. The 3D effective theory exhibits gapped and ungapped phases, which we argue are holographically dual, respectively, to a supersymmetric soliton in AdS$_{5}\times S^{5}$, and a particular quotient of AdS$_5\times S^5$. The gapped phase corresponds to an IR 3D $\mathcal{N}=2$ supersymmetric Yang-Mills-Chern-Simons theory at level $N$, while the ungapped phase is naturally identified with the root of a Higgs branch in the 3D theory. We discuss the extension of the twisting procedure to maximally SUSY Yang-Mills theories in different dimensions, obtaining the relevant duals for 2D and 6D, and comment on the odd dimensional cases.

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arXiv2023

The Holographic Map of an Evaporating Black Hole

We construct a holographic map that takes the semi-classical state of an evaporating black hole and its Hawking radiation to a microscopic model that reflects the scrambling dynamics of the black hole. The microscopic model is given by a nested sequence of random unitaries, each one implementing a scrambling time step of the black hole evolution. Differently from other models, energy conservation and the thermal nature of the Hawking radiation are taken into account. We show that the QES formula follows for the entropy of multiple subsets of the radiation and black hole. We further show that a version of entanglement wedge reconstruction can be proved by computing suitable trace norms and quantum fidelities involving the action of a unitary on a subset of Hawking partners. If the Hawking partner is in an island, its unitary can be reconstructed by a unitary on the radiation. We also adopt a similar setup and analyse reconstruction of unitaries acting on an infalling system.

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arXiv2022

Black Hole Information Recovery in JT Gravity

We consider the issue of information recovery for an object carrying energy and entropy into a black hole using the generalized entropy formalism, in the context of JT gravity where the backreaction problem can be solved exactly. We verify the main aspects of the Hayden-Preskill scenario but with some refinements. We show that the information is encoded in the Hawking radiation in a redundant way, as expected for a quantum error correcting code. We show how quantum extremal surfaces associated to information recovery have the form of a python's lunch and thereby show that the complexity of decoding is exponential in a combination of the entropy shift of the black hole and the entropy of the object. We also show that an infalling observer must have a smooth experience at the horizon and we calculate their endurance proper time inside the black hole before they are radiated out.

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arXiv2021

Grey-body Factors, Irreversibility and Multiple Island Saddles

We consider the effect of grey-body factors on the entanglement island prescription for computing the entropy of an arbitrary subset of the Hawking radiation of an evaporating black hole. When there is a non-trivial grey-body factor, the modes reflected back into the black hole affect the position of the quantum extremal surfaces at a subleading level with respect to the scrambling time. The grey-body factor allows us to analyse the role of irreversibility in the evaporation. In particular, we show that irreversibility allows multiple saddles to dominate the entropy, rather than just two as expected on the basis of Page's theorem. We show that these multiple saddles can be derived from a generalization of Page's theorem that involves a nested temporal sequence of unitary averages. We then consider how irreversibility affects the monogamy entanglement problem.

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arXiv2021

Ephemeral Islands, Plunging Quantum Extremal Surfaces and BCFT channels

We consider entanglement entropies of finite spatial intervals in Minkowski radiation baths coupled to the eternal black hole in JT gravity, and the related problem involving free fermion BCFT in the thermofield double state. We show that the non-monotonic entropy evolution in the black hole problem precisely matches that of the free fermion theory in a high temperature limit, and the results have the form expected for CFTs with quasiparticle description. Both exhibit rich behaviour that involves at intermediate times, an entropy saddle with an island in the former case, and in the latter a special class of disconnected OPE channels. The quantum extremal surfaces start inside the horizon, but can emerge from and plunge back inside as time evolves, accompanied by a characteristic dip in the entropy also seen in the free fermion BCFT. Finally an entropy equilibrium is reached with a no-island saddle.

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arXiv2021

Holographic Coulomb Branch Solitons, Quasinormal Modes, and Black Holes

Four-dimensional $\mathcal{N}=4$ supersymmetric Yang-Mills theory, at a point on the Coulomb branch where $SU(N)$ gauge symmetry is spontaneously broken to $SU(N-1)\times U(1)$, admits BPS solitons describing a spherical shell of electric and/or magnetic charges enclosing a region of unbroken gauge symmetry. These solitons have been proposed as gauge theory models for certain features of asymptotically flat extremal black holes. In the 't Hooft large $N$ limit with large 't Hooft coupling, these solitons are holographically dual to certain probe D3-branes in the $AdS_5 \times S^5$ solution of type IIB supergravity. By studying linearised perturbations of these D3-branes, we show that the solitons support quasinormal modes with a spectrum of frequencies sharing both qualitative and quantitative features with asymptotically flat extremal black holes.

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arXiv2021

Islands in the Stream of Hawking Radiation

We consider the island formula for the entropy of subsets of the Hawking radiation in the adiabatic limit where the evaporation is very slow. We find a simple concrete `on-shell' formula for the generalized entropy which involves the image of the island out in the stream of radiation, the `island in the stream'. The resulting recipe for the entropy allows us to calculate the quantum information properties of the radiation and verify various constraints including the Araki-Lieb inequality and strong subadditivity.

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arXiv2020

Holographic Entanglement Entropy of the Coulomb Branch

We compute entanglement entropy (EE) of a spherical region in $(3+1)$-dimensional $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory in states described holographically by probe D3-branes in $AdS_5 \times S^5$. We do so by generalising methods for computing EE from a probe brane action without having to determine the probe's back-reaction. On the Coulomb branch with $SU(N)$ broken to $SU(N-1)\times U(1)$, we find the EE monotonically decreases as the sphere's radius increases, consistent with the $a$-theorem. The EE of a symmetric-representation Wilson line screened in $SU(N-1)$ also monotonically decreases, although no known physical principle requires this. A spherical soliton separating $SU(N)$ inside from $SU(N-1)\times U(1)$ outside had been proposed to model an extremal black hole. However, we find the EE of a sphere at the soliton's radius does not scale with the surface area. For both the screened Wilson line and soliton, the EE at large radius is described by a position-dependent W-boson mass as a short-distance cutoff. Our holographic results for EE and one-point functions of the Lagrangian and stress-energy tensor show that at large distance the soliton looks like a Wilson line in a direct product of fundamental representations.

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arXiv2020

Islands and Page Curves for Evaporating Black Holes in JT Gravity

The effect of a CFT shockwave on the entanglement structure of an eternal black hole in Jackiw-Teitelboim gravity, that is in thermal equilibrium with a thermal bath, is considered. The shockwave carries energy and entropy into the black hole and heats the black hole up leading to evaporation and the eventual recovery of equilibrium. We find an analytical description of the entire relaxational process within the semiclassical high temperature regime. If the shockwave is inserted around the Page time then several scenarios are possible depending on the parameters. The Page time can be delayed or hastened and there can be more than one transition. The final entropy saddle has a quantum extremal surface that generically starts inside the horizon but at some later time moves outside. In general, increased shockwave energy and slow evaporation rate favour the extremal surface to be inside the horizon. The shockwave also disrupts the scrambling properties of the black hole. The same analysis is then applied to a shockwave inserted into the extremal black hole with similar conclusions.

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arXiv2020

Hawking Radiation Correlations of Evaporating Black Holes in JT Gravity

We consider the Hawking radiation emitted by an evaporating black hole in JT gravity and compute the entropy of arbitrary subsets of the radiation in the slow evaporation limit, and find a zoo of possible island saddles. The Hawking radiation is shown to have long range correlations. We compute the mutual information between early and late modes and bound from below their squashed entanglement. A small subset of late modes are shown to be correlated with modes in a suitably large subset of the radiation previously emitted as well as later modes. We show how there is a breakdown of the semi-classical approximation in the form of a violation of the Araki-Lieb triangle entropy inequality, if the interior of the black hole and the radiation are considered to be separate systems. Finally, we consider how much of the radiation must be collected, and how early, to recover information thrown into the black hole as it evaporates.

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arXiv2019

Abelian Chern-Simons vortices at finite chemical potential

We examine vortices in Abelian Chern-Simons theory coupled to a relativistic scalar field with a chemical potential for particle number or U(1) charge. The Gauss constraint requires chemical potential for the local symmetry to be accompanied by a constant background charge density/magnetic field. Focussing attention on power law scalar potentials $\sim|Φ|^{2s}$ which do not support vortex configurations in vacuum but do so at finite chemical potential, we numerically study classical vortex solutions for large winding number |n| >> 1. The solutions depending on a single dimensionless parameter $α$, behave as uniform incompressible droplets with radius $\sim \sqrt {α|n|}$ , and energy scaling linearly with |n|, independent of coupling constant. In all cases, the vortices transition from type I to type II at a critical value of the dimensionless parameter, $α_c = s/(s-1)$, which we confirm with analytical arguments and numerical methods.

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arXiv2019

Chaos bound in Bershadsky-Polyakov theory

We consider two dimensional conformal field theory (CFT) with large central charge c in an excited state obtained by the insertion of an operator Φwith large dimension Δ_Φ~ O(c) at spatial infinities in the thermal state. We argue that correlation functions of light operators in such a state can be viewed as thermal correlators with a rescaled effective temperature. The effective temperature controls the growth of out-of-time order (OTO) correlators and results in a violation of the universal upper bound on the associated Lyapunov exponent when Δ_Φ<0 and the CFT is nonunitary. We present a specific realization of this situation in the holographic Chern-Simons formulation of a CFT with {W}^{(2)}_3 symmetry also known as the Bershadsky-Polyakov algebra. We examine the precise correspondence between the semiclassical (large-c) representations of this algebra and the Chern-Simons formulation, and infer that the holographic CFT possesses a discretuum of degenerate ground states with negative conformal dimension Δ_Φ=- c/8. Using the Wilson line prescription to compute entanglement entropy and OTO correlators in the holographic CFT undergoing a local quench, we find the Lyapunov exponent λ_L = 4π/ β, violating the universal chaos bound.

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arXiv2018

Roton-phonon excitations in Chern-Simons matter theory at finite density

We consider SU(N) Chern-Simons theory coupled to a scalar field in the fundamental representation at strictly zero temperature and finite chemical potential for the global U(1)_B particle number or flavour symmetry. In the semiclassical regime we identify a Bose condensed ground state with a vacuum expectation value (VEV) for the scalar accompanied by noncommuting background gauge field matrix VEVs. These matrices coincide with the droplet ground state of the Abelian quantum Hall matrix model. The ground state spontaneously breaks U(1)_B and Higgses the gauge group whilst preserving spatial rotations and a colour-flavour locked global U(1) symmetry. We compute the perturbative spectrum of semiclassical fluctuations for the SU(2) theory and show the existence of a single massless state with a linear phonon dispersion relation and a roton minimum (and maximum) determining the Landau critical superfluid velocity. For the massless scalar theory with vanishing self interactions, the semiclassical dispersion relations and location of roton extrema take on universal forms.

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