Euclidean wormholes in two-dimensional CFTs from quantum chaos and number theory

TL;DR

This paper explores how quantum chaos and number theory constraints in 2D CFTs lead to Euclidean wormholes in AdS3 gravity, revealing deep connections between spectral correlations, modular invariance, and gravitational topology.

Contribution

It demonstrates that spectral correlations in chaotic 2D CFTs are governed by the Kuznetsov trace formula, linking quantum chaos, number theory, and Euclidean wormholes in a novel way.

Findings

Spectral form factor exhibits linear growth constrained by modular invariance.

Kuznetsov trace formula determines subleading corrections to spectral correlations.

Euclidean wormholes in AdS3 correspond to the simplest consistent CFT correlations.

Abstract

We consider two-dimensional conformal field theories (CFTs), which exhibit a hallmark feature of quantum chaos: universal repulsion of energy levels as described by a regime of linear growth of the spectral form factor. This physical input together with modular invariance strongly constrains the spectral correlations and the subleading corrections to the linear growth. We show that these are determined by the Kuznetsov trace formula, which highlights an intricate interplay of universal physical properties of chaotic CFTs and analytic number theory. The trace formula manifests the fact that the simplest possible CFT correlations consistent with quantum chaos are precisely those described by a Euclidean wormhole in AdS${}_3$ gravity with [torus]$\times$[interval] topology. For contrast, we also discuss examples of non-chaotic CFTs in this language.