More Comments on String Theory on AdS_3

TL;DR

This paper clarifies key issues in string theory on AdS_3 by constructing vertex operators and analyzing their Ward identities within the SL(2) WZW model, connecting worldsheet and spacetime perspectives.

Contribution

It introduces explicit constructions of vertex operators and spacetime symmetry generators in the interacting SL(2) WZW theory, advancing the understanding of AdS_3 string dynamics.

Findings

Constructed vertex operators for spacetime current algebra

Derived Ward identities for these operators

Clarified the relation between worldsheet and spacetime descriptions

Abstract

We clarify a number of issues regarding the worldsheet and spacetime descriptions of string propagation on AdS_3. We construct the vertex operators of spacetime current algebra and spacetime (super) Virasoro generators in the full interacting SL(2) WZW theory and study their Ward identities. We also explain the relation between the analysis in this note and some recent work on this subject.