| Summary: | Abstract In this note, we comment on the path integral formulation of string theory on M $$ \mathcal{M} $$ × S3 × T 4 $$ {\mathbbm{T}}^4 $$ where M $$ \mathcal{M} $$ 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 $$ \partial \mathcal{M} $$ , 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 $$ \mathcal{M} $$ , 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.
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