Spacetime Virasoro algebra from strings on zero radius AdS_3

TL;DR

This paper explores bosonic string theory on zero-radius AdS_3, revealing an infinite set of conserved charges forming a Virasoro algebra, linking worldsheet symmetries to spacetime asymptotic symmetries and suggesting a duality with free field theories.

Contribution

It demonstrates the emergence of a spacetime Virasoro algebra from string theory in zero-radius AdS_3 and connects worldsheet and spacetime symmetries, extending the understanding of AdS/CFT correspondence.

Findings

Spacetime charges form a Virasoro algebra near AdS_3 boundary.

Worldsheet Virasoro algebra can have a central extension.

Spacetime Virasoro algebra is isomorphic to Brown-Henneaux asymptotic symmetries.

Abstract

We study bosonic string theory in the light-cone gauge on AdS_3 spacetime with zero radius of curvature (in string units) R/\sqrt{\alpha^\prime}=0. We find that the worldsheet theory admits an infinite number of conserved quantities which are naturally interpreted as spacetime charges and which form a representation of (two commuting copies of) a Virasoro algebra. Near the boundary of AdS_3 these charges are found to be isomorphic to the infinite set of asymptotic Killing vectors of AdS_3 found originally by Brown and Henneaux. In addition to the spacetime Virasoro algebra, there is a worldsheet Virasoro algebra that generates diffeomorphisms of the spatial coordinate of the string worldsheet. We find that if the worldsheet Virasoro algebra has a central extension then the spacetime Virasoro algebra acquires a central extension via a mechanism similar to that encountered in the context of the SL(2,R) WZW model.Our observations are consistent with a recently proposed duality between bosonic strings on zero radius AdS_d+1 and free field theory in d dimensions.