A note on background independence in AdS 3 string theory

Abstract

In this note, we comment on the path integral formulation of string theory on M × S3 × T4 where M is any hyperbolic 3-manifold. In the special case of k = 1 units of NS-NS flux, we provide a covariant description of the worldsheet theory and argue that the path integral depends only on the details of the conformal boundary ∂M, making the background independence of this theory manifest. We provide a simple path integral argument that the path integral localizes onto holomorphic covering maps from the worldsheet to the boundary. For closed manifolds M, the gravitational path integral is argued to be trivial. Finally, we comment on the effect of continuous deformations of the worldsheet theory which introduce non-minimal string tension.