Alexander Altland, Boris Post, Julian Sonner, Jeremy van der Heijden, Erik Verlinde
SciPost Phys. 15, 064 (2023) ·
published 16 August 2023

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We present a quantitative and fully nonperturbative description of the ergodic phase of quantum chaos in the setting of twodimensional gravity. To this end we describe the doubly nonperturbative completion of semiclassical 2D gravity in terms of its associated universe field theory. The guiding principle of our analysis is a flavormatrix theory (fMT) description of the ergodic phase of holographic gravity, which exhibits $\mathrm{U}(nn)$ causal symmetry breaking and restoration. JT gravity and its 2Dgravity cousins alone do not realize an action principle with causal symmetry, however we demonstrate that their universe field theory, the KodairaSpencer (KS) theory of gravity, does. After directly deriving the fMT from braneantibrane correlators in KS theory, we show that causal symmetry breaking and restoration can be understood geometrically in terms of different (topological) Dbrane vacua. We interpret our results in terms of an openclosed string duality between holomorphic ChernSimons theory and its closedstring 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.
SciPost Phys. 11, 034 (2021) ·
published 18 August 2021

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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 symmetrybreaking principle and its associated Goldstone modes. This allows us to write down an effectivefield theory (EFT) description of quantum chaotic systems, which is able to control the level statistics up to an accuracy ${\cal O} \left(e^{S} \right)$ with $S$ 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 higherdimensional AdS/CFT dual pairs.