String Theory on AdS_3

TL;DR

This paper investigates the realization of Virasoro symmetry in string theory on AdS_3, connecting classical gravity results with string-theoretic constructions and clarifying the emergence of boundary conformal symmetry.

Contribution

It elucidates how the Virasoro algebra from gravity is realized in string theory, analyzing the GKS construction and boundary symmetry realization.

Findings

Virasoro symmetry is realized in string theory on AdS_3.

The GKS Virasoro generators naturally emerge in the analysis.

The central charge generation mechanism differs from previous proposals.

Abstract

It was shown by Brown and Henneaux that the classical theory of gravity on AdS_3 has an infinite-dimensional symmetry group forming a Virasoro algebra. More recently, Giveon, Kutasov and Seiberg (GKS) constructed the corresponding Virasoro generators in the first-quantized string theory on AdS_3. In this paper, we explore various aspects of string theory on AdS_3 and study the relation between these two works. We show how semi-classical properties of the string theory reproduce many features of the AdS/CFT duality. Furthermore, we examine how the Virasoro symmetry of Brown and Henneaux is realized in string theory, and show how it leads to the Virasoro Ward identities of the boundary CFT. The Virasoro generators of GKS emerge naturally in this analysis. Our work clarifies several aspects of the GKS construction: why the Brown-Henneaux Virasoro algebra can be realized on the first-quantized Hilbert space, to what extent the free-field approximation is valid, and why the Virasoro generators act on the string worldsheet localized near the boundary of AdS_3. On the other hand, we find that the way the central charge of the Virasoro algebra is generated is different from the mechanism proposed by GKS.