We present a quantitative and fully non-perturbative description of the ergodic phase of quantum chaos in the setting of two-dimensional gravity. To this end we describe the doubly non-perturbative ...completion of semiclassical 2D gravity in terms of its associated universe field theory. The guiding principle of our analysis is a flavor-matrix theory (fMT) description of the ergodic phase of holographic gravity, which exhibits
\mathrm{U}(n|n)
U
(
n
|
n
)
causal symmetry breaking and restoration. JT gravity and its 2D-gravity cousins alone do not realize an action principle with causal symmetry, however we demonstrate that their universe field theory, the Kodaira-Spencer (KS) theory of gravity, does. After directly deriving the fMT from brane-antibrane correlators in KS theory, we show that causal symmetry breaking and restoration can be understood geometrically in terms of different (topological) D-brane vacua. We interpret our results in terms of an open-closed string duality between holomorphic Chern-Simons theory and its closed-string equivalent, the KS theory of gravity. Emphasis will be put on relating these geometric principles to the characteristic spectral correlations of the quantum ergodic phase.
Probing typical black hole microstates de Boer, Jan; van Breukelen, Rik; Lokhande, Sagar F. ...
The journal of high energy physics,
01/2020, Letnik:
2020, Številka:
1
Journal Article
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A
bstract
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.
A
bstract
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
˜
, where
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.
A
bstract
It was recently argued in
1
that black hole complementarity strains the basic rules of quantum information theory, such as monogamy of entanglement. Motivated by this argument, we develop ...a practical framework for describing black hole evaporation via unitary time evolution, based on a holographic perspective in which all black hole degrees of freedom live on the stretched horizon. We model the horizon as a unitary quantum system with finite entropy, and
do not postulate that the horizon geometry is smooth
. We then show that, with mild assumptions, one can reconstruct local effective field theory observables that probe the black hole interior, and relative to which the state near the horizon looks like a local Minkowski vacuum. The reconstruction makes use of the formalism of quantum error correcting codes, and works for black hole states whose entanglement entropy does not yet saturate the Bekenstein-Hawking bound. Our general framework clarifies the black hole final state proposal, and allows a quantitative study of the transition into the “firewall” regime of maximally mixed black hole states.
We show that the partition function of free Maxwell theory on a generic eulidean four-manifold transforms in a non-trivial way under electric-magnetic duality. The classical part of the partition sum ...can be mapped onto the genus-one partition function of a 2D toroidal model, without the oscillator contributions. This map relates electric-magnetic duality to modular invariance of the toroidal model and, conversely, the O(
d,
d′,
Z) duality to the invariance of Maxwell theory under the 4D mapping class group. The dualities and the relation between toroidal models and Maxwell theory can be understood by regarding both theories as dimensional reductions of a self-dual 2-form theory in six dimensions. Generalizations to more U(1)-gauge fields and reductions from higher dimensions are also discussed. We find indications that the abelian gauge theories with
N = 4 space-time supersymmetry are exactly duality invariant.
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