On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles

TL;DR

This paper classifies all semiclassical saddles contributing to Virasoro blocks at large central charge, revealing that most decay exponentially at late times, but some sub-leading saddles do not, impacting the understanding of information loss in AdS3.

Contribution

It provides a comprehensive classification of all relevant saddles for Virasoro blocks in the semiclassical limit, including non-decaying sub-leading saddles.

Findings

Leading saddles decay exponentially at late times

Most high-energy contributions do not resolve information loss

Some sub-leading saddles do not decay, affecting black hole information paradox

Abstract

Recent work has demonstrated that black hole thermodynamics and information loss/restoration in AdS$_3$/CFT$_2$ can be derived almost entirely from the behavior of the Virasoro conformal blocks at large central charge, with relatively little dependence on the precise details of the CFT spectrum or OPE coefficients. Here, we elaborate on the non-perturbative behavior of Virasoro blocks by classifying all `saddles' that can contribute for arbitrary values of external and internal operator dimensions in the semiclassical large central charge limit. The leading saddles, which determine the naive semiclassical behavior of the Virasoro blocks, all decay exponentially at late times, and at a rate that is independent of internal operator dimensions. Consequently, the semiclassical contribution of high-energy states does not resolve a well-known version of the information loss problem in AdS$_3$. However, we identify two infinite classes of sub-leading saddles, and one of these classes does not decay at late times.