Supergroup Structure of Jackiw-Teitelboim Supergravity

TL;DR

This paper formulates $ ext{OSp}(1|2, eals)$ supergravity as a gauge theory, linking boundary dynamics to super-Schwarzian quantum mechanics, classifying defects, and analyzing the density of states and complexity growth.

Contribution

It develops a gauge theory framework for $ ext{OSp}(1|2, eals)$ supergravity, connecting BF theory to super-Schwarzian mechanics and analyzing the representation theory and density of states.

Findings

BF description reduces to super-Schwarzian quantum mechanics.

Classification of defects via monodromies in $ ext{OSp}(1|2, eals)$.

Restriction to positive subsemigroup yields correct density of states.

Abstract

We develop the gauge theory formulation of $\mathcal{N}=1$ Jackiw-Teitelboim supergravity in terms of the underlying $\text{OSp}(1|2, \mathbb{R})$ supergroup, focusing on boundary dynamics and the exact structure of gravitational amplitudes. We prove that the BF description reduces to a super-Schwarzian quantum mechanics on the holographic boundary, where boundary-anchored Wilson lines map to bilocal operators in the super-Schwarzian theory. A classification of defects in terms of monodromies of $\text{OSp}(1|2, \mathbb{R})$ is carried out and interpreted in terms of character insertions in the bulk. From a mathematical perspective, we construct the principal series representations of $\text{OSp}(1|2, \mathbb{R})$ and show that whereas the corresponding Plancherel measure does not match the density of states of $\mathcal{N}=1$ JT supergravity, a restriction to the positive subsemigroup $\text{OSp}^+(1|2, \mathbb{R})$ yields the correct density of states, mirroring the analogous results for bosonic JT gravity. We illustrate these results with several gravitational applications, in particular computing the late-time complexity growth in JT supergravity.