The Super Virasoro Minimal String from 3d Supergravity

The super Virasoro minimal string is defined by coupling spacelike and timelike super Liouville theories on the worldsheet. There are four different theories 0A${}^{\pm }$ and 0B${}^{\pm }$ depending on discrete choices on the worldsheet. We show that these theories arise naturally from quantization of 3d supergravity, and the amplitudes compute the dimension ($+$) or superdimension ($-$) of the space of $\mathcal{N}=1$ superconformal blocks modulo crossing symmetry. Both 0A${}^{+}$ and 0B${}^{+}$ are perturbatively dual to the same matrix integral as the bosonic Virasoro minimal string, while 0B${}^{-}$ is dual to a matrix integral with an inverse square root singularity. We show that all non-trivial perturbative amplitudes of the 0A${}^{-}$ theory vanish.