3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator

Abstract

In this paper, we compute the partition functions of $\mathcal{N}=1$ SUGRA for different boundary topologies, i.e. \textcolor{black}{punctured sphere} and torus, using super-Virasoro TQFT. We use fusion and modular kernels of the super-Liouville theory to compute the necklace-channel conformal block and showcase formalism by proving that the inner product holds for superconformal blocks, defined as states in the Hilbert space. Finally, we compute the out-of-time-order correlator for the torus topology with superconformal primary insertions as matter using the tools of super-Virasoro TQFT.

Minor typos corrected

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