Symmetries and spectral statistics in chaotic conformal field theories

Abstract

We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic properties of the spectrum from those which are a consequence of Virasoro symmetry and modular invariance. We argue that random matrix universality in the near-extremal limit is an independent feature of each spin sector separately; this is a non-trivial statement because the exact spectrum is fully determined by only the spectrum of spin zero primaries and those of a single non-zero spin ("spectral determinacy"). We then describe an argument analogous to the one leading to Cardy's formula for the averaged density of states, but in our case applying it to spectral correlations: assuming statistical universalities in the near-extremal spectrum in all spin sectors, we find similar random matrix universality in a large spin regime far from extremality.

arXiv comment35 pages, 5 figures. v2: corrected statements about the role of Maass cusp forms. v3: minor change in discussion of spin 0 SFF. v4: very minor corrections

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• Multiboundary wormholes and OPE statistics
• Symmetries and spectral statistics in chaotic conformal field theories
• 3d Gravity as a random ensemble
• Euclidean wormholes in two-dimensional CFTs from quantum chaos and number theory
• Symmetries and spectral statistics in chaotic conformal field theories II: Maass cusp forms and arithmetic chaos
• Modular-invariant random matrix theory and AdS${}_3$ wormholes
• Rademacher expansion of modular integrals
• A universal sum over topologies in 3d gravity