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

TL;DR

This paper computes the partition functions of 3D $ abla=1$ supergravity on different topologies using super-Virasoro TQFT, and analyzes out-of-time-order correlators to explore quantum chaos in this setting.

Contribution

It introduces a formalism for super-Virasoro TQFT to compute supergravity partition functions and out-of-time-order correlators, extending previous methods to supersymmetric theories.

Findings

Partition functions for sphere and torus topologies computed.

Validated the inner product for superconformal blocks.

Analyzed early-time behavior of out-of-time-order correlators.

Abstract

In this paper, we compute the partition functions of $\mathcal{N}=1$ SUGRA for different boundary topologies, i.e. 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 and investigate its early-time behaviour.