  In this note, we comment on the path integral formulation of string theory on
$\mathcal{M}\times\text{S}^3\times\mathbb{T}^4$ where $\mathcal{M}$ is any
hyperbolic 3-manifold. In the special case of $k=1$ 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 $\partial\mathcal{M}$,
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
$\mathcal{M}$, the gravitational path integral is argued to be trivial. This
implies that the bulk gravitational theory has precisely one state in its
Hilbert space. Finally, we comment on the effect of continuous deformations of
the worldsheet theory which introduce non-minimal string tension.
