AdS$_3$/RMT$_2$ Duality - Archive ouverte HAL
Article Dans Une Revue Journal of High Energy Physics Année : 2023

AdS$_3$/RMT$_2$ Duality

Résumé

We introduce a framework for quantifying random matrix behavior of 2d CFTs and AdS$_3$ quantum gravity. We present a 2d CFT trace formula, precisely analogous to the Gutzwiller trace formula for chaotic quantum systems, which originates from the $SL(2,\mathbb{Z})$ spectral decomposition of the Virasoro primary density of states. An analogy to Berry's diagonal approximation allows us to extract spectral statistics of individual 2d CFTs by coarse-graining, and to identify signatures of chaos and random matrix universality. This leads to a necessary and sufficient condition for a 2d CFT to display a linear ramp in its coarse-grained spectral form factor. Turning to gravity, AdS$_3$ torus wormholes are cleanly interpreted as diagonal projections of squared partition functions of microscopic 2d CFTs. The projection makes use of Hecke operators. The Cotler-Jensen wormhole of AdS$_3$ pure gravity is shown to be extremal among wormhole amplitudes: it is the minimal completion of the random matrix theory correlator compatible with Virasoro symmetry and $SL(2,\mathbb{Z})$-invariance. We call this MaxRMT: the maximal realization of random matrix universality consistent with the necessary symmetries. Completeness of the $SL(2,\mathbb{Z})$ spectral decomposition as a trace formula allows us to factorize the Cotler-Jensen wormhole, extracting the microscopic object $Z_{\rm RMT}(\tau)$ from the coarse-grained product. This captures details of the spectrum of BTZ black hole microstates. $Z_{\rm RMT}(\tau)$ may be interpreted as an AdS$_3$ half-wormhole. We discuss its implications for the dual CFT and modular bootstrap at large central charge.

Dates et versions

hal-04161876 , version 1 (13-07-2023)

Identifiants

Citer

Gabriele Di Ubaldo, Eric Perlmutter. AdS$_3$/RMT$_2$ Duality. Journal of High Energy Physics, 2023, 12, pp.179. ⟨10.1007/JHEP12(2023)179⟩. ⟨hal-04161876⟩
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