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arXiv:1901.08527 · Journal of High Energy Physics

Probing typical black hole microstates

Jan De Boer A, Rik van Breukelen, Sagar F. Lokhande, Kyriakos Papadodimas, Erik Verlinde

Published Jan 1, 2020• 30 citations
arXivHTMLPDF

Abstract

Abstract We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model and discuss similarities with state-dependent perturba- tions of pure states in the SYK model previously considered by Kourkoulou and Maldacena. Finally, we discuss how the mirror operators can be used to implement an analogue of the Hayden-Preskill protocol.

DOI
10.1007/jhep01(2020)062

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Abstract We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model and discuss similarities with state-dependent perturba- tions of pure states in the SYK model previously considered by Kourkoulou and Maldacena. Finally, we discuss how the mirror operators can be used to implement an analogue of the Hayden-Preskill protocol.
Abstract We argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a deformation of the CFT Hamiltonian by a term of the form OO~ \mathcal{O}\tilde{\mathcal{O}} OO~ O O ˜ , where O~ \tilde{\mathcal{O}} O~ O ˜ denote the state-dependent “mirror operators”. We argue that this deformation creates negative energy shockwaves in the bulk, which allow particles inside the horizon to escape and to get directly detected in the CFT. This provides evidence for the smoothness of the horizon of black holes dual to typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.
We argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a deformation of the CFT Hamiltonian by a term of the form O O ˜ mathcalOtildemathcalO \\mathcal{O}\\tilde{\\mathcal{O}} mathcalOtildemathcalO , where O ˜ tildemathcalO \\tilde{\\mathcal{O}} tildemathcalO denote the state-dependent “mirror operators”. We argue that this deformation creates negative energy shockwaves in the bulk, which allow particles inside the horizon to escape and to get directly detected in the CFT. This provides evidence for the smoothness of the horizon of black holes dual to typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.
Via holographic duality (or ‘AdS/CFT'), the process of black hole formation and evaporation corresponds to the process of thermalization of certain (unitary) quantum field theories, evolving from non-equilibrium initial states towards thermal equilibrium. In this context, the question of how thermal a generic high-energy eigenstate looks in a theory with a holographic dual is closely tied to the question of how legitimately one may consider the dual geometry of this pure state to be a black hole. In this thesis we present some results which shed light on the nature of this relationship, through a detailed study of the dynamics of the so-called SYK model —a holographic, many-body quantum mechanical system of interacting fermions. The results indicate that this model satisfies the eigenstate thermalization hypothesis, which we extend to explore its implications on certain quantum chaotic properties the SYK Hamiltonian that mirror the quantum chaotic behavior of black holes.
We demonstrate that the Euclidean two-point function of an appropriately chosen probe operator can detect the microstate of an asymptotically AdS black hole. This detection, which requires a tuned, state-dependent choice of probe, is the result of a new gravitational saddle, which dominates over the usual saddles. The gravitational result can be explicitly reproduced in the dual boundary CFT if we assume the eigenstate thermalization hypothesis. We also discuss a binary search protocol to detect the black hole microstate from a candidate list.
We consider a class of non-equilibrium pure states, which are generally present in an isolated quantum statistical system. These are states of the form ∣Ψ⟩=e−βH2UeβH2∣Ψ0⟩|Ψ\rangle=e^{-{βH \over 2}} U e^{βH \over 2} |Ψ_0\rangle∣Ψ⟩=e−2βH​Ue2βH​∣Ψ0​⟩, where UUU is a unitary made out of simple operators and ∣Ψ0⟩|Ψ_0\rangle∣Ψ0​⟩ is a typical equilibrium pure state with sharply peaked energy. We argue that in a system with a holographic dual these states have a natural interpretation as an AdS black hole with transient excitations behind the horizon. We explore the interpretation of these states as pure states undergoing a time-dependent spontaneous fluctuation out of equilibrium. While these states are atypical and the microscopic phases of the wavefunction are correlated with the matrix elements of simple operators, the states are partly disguised as equilibrium states due to cancellations between contributions from different coarse-grained energy bins. These cancellations are guaranteed by the KMS condition of the underlying equilibrium state ∣Ψ0⟩|Ψ_0\rangle∣Ψ0​⟩. However, in correlators which include the Hamiltonian HHH these cancellations are spoiled and the non-equilibrium nature of the state ∣Ψ⟩|Ψ\rangle∣Ψ⟩ can be detected. We discuss connections with the proposal that local observables behind the horizon are realized as state-dependent operators. The states studied in this paper may be useful for implementing an analogue of the "traversable wormhole" protocol for a 1-sided black hole, which could potentially allow us to extract the excitation from behind the horizon. We include some pedagogical background material.
Abstract We study various aspects of the mass deformation of the SYK model which makes the black hole microstates escapable. SYK boundary states are given by a simple local boundary condition on the Majorana fermions and then evolved in Euclidean time in the SYK Hamiltonian. We study the ground state of this mass deformed SYK model in detail. We also use SYK boundary states as a variational approximation to the ground state of the mass deformed SYK model. We compare variational approximation with the exact ground state results and they showed a good agreement. We also study the time evolution of the mass deformed ground state under the SYK Hamiltonian. We give a gravity interpretation of the mass deformed ground state and its time evolutions. In gravity side, mass deformation gives a way to prepare black hole microstates that are similar to pure boundary state black holes. Escaping protocol on these ground states simply gives a global AdS2 with an IR end of the world brane. We also study the thermodynamics and quantum chaotic properties of this mass deformed SYK model. Interestingly, we do not observe the Hawking Page like phase transition in this model in spite of similarity of the Hamiltonian with eternal traversable wormhole model where we have the phase transition.