Asymptotically Free AdS3/CFT2

TL;DR

This paper introduces a new AdS3/CFT2 duality involving a string theory on a squashed three-sphere and a deformed symmetric product CFT, providing insights into string/black hole transition regimes.

Contribution

It proposes a novel duality with a specific bulk geometry and boundary theory, analyzing the string theory on AdS3 to derive the dual CFT2 in a new regime.

Findings

High energy states are string gases, not black holes.

Duality maps asymptotic AdS3 to a region where twist interactions vanish.

Provides a systematic derivation of the dual CFT from worldsheet string theory.

Abstract

We propose a new $AdS_3/CFT_2$ duality, in which the bulk string theory has a target spacetime $AdS_3$ times a squashed three-sphere $S^3_\flat$, and the dual $CFT_2$ is a symmetric product of sigma models on $R_\phi\times S^3_\flat$, deformed by a $\phi$-dependent $Z_2$ twist operator. The duality maps the asymptotic region of $AdS_3$ to the region $\phi\to\infty$, where the twist interaction in the $CFT_2$ turns off. The $AdS_3$ backgrounds in question have $R_{AdS}<\ell_s$, and so lie on the string side of the string/black hole correspondence transition. As a consequence, the high energy density of states consists of a string gas in $AdS_3$ rather than an ensemble of BTZ black holes. This property allows us to derive the dual $CFT_2$ by a systematic analysis of the worldsheet string theory on $AdS_3$.