Late time physics of holographic quantum chaos

Abstract

Quantum chaotic systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, random matrix theory. In this paper we explain how the universal content of random matrix theory emerges as the consequence of a simple symmetry-breaking principle and its associated Goldstone modes. This allows us to write down an effective-field theory (EFT) description of quantum chaotic systems, which is able to control the level statistics up to an accuracy {O} \left(e^{-S} \right)O(e−S) with SS the entropy. We explain how the EFT description emerges from explicit ensembles, using the example of a matrix model with arbitrary invariant potential, but also when and how it applies to individual quantum systems, without reference to an ensemble. Within AdS/CFT this gives a general framework to express correlations between ``different universes’’ and we explicitly demonstrate the bulk realization of the EFT in minimal string theory where the Goldstone modes are bound states of strings stretching between bulk spectral branes. We discuss the construction of the EFT of quantum chaos also in higher dimensional field theories, as applicable for example for higher-dimensional AdS/CFT dual pairs.

Islands with gravitating baths: towards ER = EPR

“…Secondly, this set-up somehow bridges recent discussions of averaging [72,80,86,90,92], quantum error correction [56,89,118] and 'third-quantized' gravity [64,84,[119][120][121]. The most obvious connection is with averaging, since the set-up of two black holes with real-time coupling was the one that was found to give the clearest demonstration of the averaged nature of semiclassical gravity [86].…”

“…In this sense, entanglement leads to a connected geometry. Another important point here is that the calculation above is unaffected by the precise structure of the entanglement between the two branes, i.e., the details of the matrix M , thus giving another example of classical gravity exhibiting averaging [72,80,86,[89][90][91][92].…”

Bootstrapping quantum extremal surfaces. Part I. The area operator

“…Precisely answering this question in the context of black hole evaporation or for highenergy dynamics is a formidable task, and strong evidence seems to suggest that the gravitational theory has only access to statistical properties of the dual CFT [14][15][16][17][18][19][20][21]. As a starting point, we will consider states that are obtained by acting with low-dimension operators on the CFT vacuum, corresponding to perturbative few-quanta excitations of the JHEP11(2021)021 quantum fields that propagate in the bulk.…”

Integrality, duality and finiteness in combinatoric topological strings

“…If there is an AdS/CFT set-up, the expectation is that the CFT partition function factorizes while from the bulk it is expected that the existence of a common bulk leads to a non-factorizing partition function. Recent discussions of the puzzle include [71][72][73][74].…”