2D CFT Partition Functions at Late Times

TL;DR

This paper investigates the late-time decay of partition functions in 2D holographic CFTs, revealing universal decay patterns, a potential crossover to random matrix behavior, and mechanisms for information restoration in integrable theories.

Contribution

It identifies universal late-time decay behavior in 2D CFT partition functions and proposes a conjecture for chaotic CFTs, including bounds on crossover times and insights into information recovery.

Findings

Virasoro characters decay at late times

Universal decaying contribution identified

Bound on crossover to random matrix behavior

Abstract

We consider the late time behavior of the analytically continued partition function $Z(\beta + it) Z(\beta - it)$ in holographic $2d$ CFTs. This is a probe of information loss in such theories and in their holographic duals. We show that each Virasoro character decays in time, and so information is not restored at the level of individual characters. We identify a universal decaying contribution at late times, and conjecture that it describes the behavior of generic chaotic $2d$ CFTs out to times that are exponentially large in the central charge. It was recently suggested that at sufficiently late times one expects a crossover to random matrix behavior. We estimate an upper bound on the crossover time, which suggests that the decay is followed by a parametrically long period of late time growth. Finally, we discuss integrable theories and show how information is restored at late times by a series of characters. This hints at a possible bulk mechanism, where information is restored by an infinite sum over non-perturbative saddles.