A Note on Classical String Dynamics on AdS_3

TL;DR

This paper explores the symmetries of bosonic strings on Euclidean AdS_3, defining the Brown-Henneaux symmetry, deriving the worldsheet contour integral, and revealing a connection between 3D gravity and string worldsheet dynamics.

Contribution

It provides a proper definition of Brown-Henneaux symmetry on the string worldsheet and links target space identifications to graviton vertex operators, connecting 3D gravity with string theory on AdS_3.

Findings

Brown-Henneaux symmetry is properly defined on the string action.

Target space identifications correspond to graviton vertex insertions.

Reduction conditions in gravity and string theory are shown to be equivalent.

Abstract

We consider bosonic strings propagating on Euclidean adS_3, and study in particular the realization of various worldsheet symmetries. We give a proper definition for the Brown-Henneaux asymptotic target space symmetry, when acting on the string action, and derive the Giveon-Kutasov-Seiberg worldsheet contour integral representation simply by using Noether's theorem. We show that making identifications in the target space is equivalent to the insertion of an (exponentiated) graviton vertex operator carrying the corresponding charge. Finally, we point out an interesting relation between 3D gravity and the dynamics of the worldsheet on adS_3. Both theories are described by an SL(2,C)/SU(2) WZW model, and we prove that the reduction conditions determined on one hand by worldsheet diffeomorphism invariance, and on the other by the Brown-Henneaux boundary conditions, are the same.