Abstract: Out-of-time-order correlators (OTOCs) that capture maximally chaotic properties of a black hole are determined by scattering processes near the horizon. This prompts the question to what extent OTOCs display chaotic behaviour in horizonless microstate geometries. This question is complicated by the fact that Lyapunov growth of OTOCs requires nonzero temperature, whereas constructions of microstate geometries have been mostly restricted to extremal black holes. In this paper, we compute OTOCs for a class of extremal black holes, namely maximally rotating BTZ black holes, and show that on average they display “slow scrambling”, characterized by cubic (rather than exponential) growth. Superposed on this average power-law growth is a sawtooth pattern, whose steep parts correspond to brief periods of Lyapunov growth associated to the nonzero temperature of the right-moving degrees of freedom in a dual conformal field theory. Next we study the extent to which these OTOCs are modified in certain “superstrata”, horizonless microstate geometries corresponding to these black holes. Rather than an infinite throat ending on a horizon, these geometries have a very deep but finite throat ending in a cap. We find that the superstrata display the same slow scrambling as maximally rotating BTZ black holes, except that for large enough time intervals the growth of the OTOC is cut off by effects related to the cap region, some of which we evaluate explicitly.

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Topics: Black hole (57%), Ministate (51%), AdS/CFT correspondence (50%)

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10 results found

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Abstract: We consider the eikonal phase associated with the gravitational scattering of a highly energetic light particle off a very heavy object in AdS spacetime. A simple expression for this phase follows from the WKB approximation to the scattering amplitude and has been computed to all orders in the ratio of the impact parameter to the Schwarzschild radius of the heavy particle. The eikonal phase is related to the deflection angle by the usual stationary phase relation. We consider the flat space limit and observe that for sufficiently small impact parameters (or angular momenta) the eikonal phase develops a large imaginary part; the inelastic cross-section is exactly the classical absorption cross-section of the black hole. We also consider a double scaling limit where the momentum becomes null simultaneously with the asymptotically AdS black hole becoming very large. In the dual CFT this limit retains contributions from all leading twist multi stress tensor operators, which are universal with respect to the addition of higher derivative terms to the gravitational lagrangian. We compute the eikonal phase and the associated Lyapunov exponent in the double scaling limit.

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Topics: AdS black hole (62%), Schwarzschild radius (60%), Eikonal equation (58%) ... show more

8 Citations

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Abstract: We study the origin of the recently proposed effective theory of stress tensor exchanges based on reparametrization modes, that has been used to efficiently compute Virasoro identity blocks at large central charge. We first provide a derivation of the nonlinear Alekseev-Shatashvili action governing these reparametrization modes, and argue that it should be interpreted as the generating functional of stress tensor correlations on manifolds related to the plane by conformal transformations. In addition, we demonstrate that the rules previously prescribed with the reparametrization formalism for computing Virasoro identity blocks naturally emerge when evaluating Feynman diagrams associated with stress tensor exchanges between pairs of external primary operators. We make a few comments on the connection of these results to gravitational theories and holography.

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Topics: Cauchy stress tensor (58%), Conformal field theory (56%), Central charge (53%) ... show more

7 Citations

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Abstract: In maximally chaotic quantum systems, a class of out-of-time-order
correlators (OTOCs) saturate the Maldacena-Shenker-Stanford (MSS) bound on
chaos. Recently, it has been shown that the same OTOCs must also obey an
infinite set of (subleading) constraints in any thermal quantum system with a
large number of degrees of freedom. In this paper, we find a unique analytic
extension of the maximally chaotic OTOC that saturates all the subleading chaos
bounds which allow saturation. This extremally chaotic OTOC has the feature
that information of the initial perturbation is recovered at very late times.
Furthermore, we argue that the extremally chaotic OTOC provides a
K\"{a}llen-Lehmann-type representation for all OTOCs. This representation
enables the identification of all analytic completions of maximal chaos as
small deformations of extremal chaos in a precise way.

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Topics: Chaotic (52%), Quantum system (51%)

2 Citations

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Abstract: We find stationary thin-brane geometries that are dual to far-from-equilibrium steady states of two-dimensional holographic interfaces. The flow of heat at the boundary agrees with the result of CFT and the known energy-transport coefficients of the thin-brane model. We argue that by entangling outgoing excitations the interface produces thermodynamic entropy at a maximal rate, and point out similarities and differences with double-sided black funnels. The non-compact, non-Killing and far-from-equilibrium event horizon of our solutions coincides with the local (apparent) horizon on the colder side, but lies behind it on the hotter side of the interface. We also show that the thermal conductivity of a pair of interfaces jumps at the Hawking-Page phase transition from a regime described by classical scatterers to a quantum regime in which heat flows unobstructed.

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Topics: Event horizon (56%), Horizon (52%), Phase transition (52%) ... show more

1 Citations

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Abstract: We use mixed correlators in thermal CFT as clean probes of the strong gravity effects in their holographic duals. The dual interpretation of mixing is an inelastic conversion of one field to another field, induced by gravity: tidal excitation. We find an enhanced mixing at high temperatures, corresponding to large AdS black holes, concentrated to small boundary momenta, dual to the deep bulk, where strong gravitational fields are expected. We also find large $$ \mathcal{O}\left(1/{G}_N\right) $$
tidal conversion in the low temperature phase of the U(N) vector model, strengthening suspicions that the bulk dual of this phase also houses extremely compact objects.

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Topics: Mixing (physics) (53%), AdS/CFT correspondence (52%), Gravitational field (51%) ... show more

1 Citations

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42 results found

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Abstract: It is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level. This is done by studying three dimensional gravity with a negative cosmological constant. The asymptotic symmetry group in that case is eitherR×SO(2) or the pseudo-conformal group in two dimensions, depending on the boundary conditions adopted at spatial infinity. In the latter situation, a nontrivial central charge appears in the algebra of the canonical generators, which turns out to be just the Virasoro central charge.

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Topics: Central charge (62%), Virasoro algebra (61%), Charge (physics) (61%) ... show more

2,762 Citations

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Abstract: We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ
L
≤ 2πk
B
T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

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Topics: Quantum chaos (61%), Lyapunov exponent (55%), Conjecture (51%)

1,601 Citations

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Abstract: We propose a dual non-perturbative description for maximally extended Schwarzschild Anti-de-Sitter spacetimes. The description involves two copies of the conformal field theory associated to the AdS spacetime and an initial entangled state. In this context we also discuss a version of the information loss paradox and its resolution.

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Topics: Black hole information paradox (57%), ER=EPR (56%), Black hole (55%) ... show more

1,508 Citations

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Stephen H. Shenker^{1}, Stephen H. Shenker^{2}, Douglas Stanford^{1}, Douglas Stanford^{2}•Institutions (2)

Abstract: We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the t = 0 slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup, and discuss points that may be relevant to the firewall controversy.

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Topics: AdS black hole (55%), Firewall (physics) (54%), AdS/CFT correspondence (51%)

1,209 Citations

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Abstract: We propose a dual non-perturbative description for maximally extended Schwarzschild Anti-de-Sitter spacetimes. The description involves two copies of the conformal field theory associated to the AdS spacetime and an initial entangled state. In this context we also discuss a version of the information loss paradox and its resolution.

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Topics: Black hole information paradox (59%), Conformal field theory (55%), Schwarzschild radius (55%) ... show more

1,014 Citations