Symmetries and spectral statistics in chaotic conformal field theories

TL;DR

This paper investigates spectral correlations in chaotic 2D conformal field theories with large central charge, revealing that random matrix universality applies independently to each spin sector, both near and far from extremality.

Contribution

It demonstrates that spectral universality in chaotic 2D CFTs is an independent feature of each spin sector, extending the understanding of spectral correlations beyond extremal limits.

Findings

Random matrix universality applies to each spin sector separately.

Spectral determinacy links the entire spectrum to spin zero primaries and one non-zero spin sector.

Universal spectral correlations are found in the large spin regime far from extremality.

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.