Branes in JT (super)gravity from group theory

TL;DR

This paper explores the group-theoretic formulation of end-of-the-world brane amplitudes in JT gravity and its supersymmetric extensions, providing explicit calculations and developing relevant representation theory.

Contribution

It identifies the correct group-theoretic ingredients for EOW branes in JT gravity and extends the framework to supersymmetric cases, including explicit amplitude computations.

Findings

Explicit supersymmetric EOW brane amplitudes computed.

Development of representation theory for OSp(2|2,R) and PSU(1,1|2).

Identification of discrete series characters as key ingredients.

Abstract

In this work, we revisit the end-of-the-world (EOW) brane amplitudes in JT gravity from a BF gauge theoretic perspective. Observing and identifying the correct group theoretic ingredient for a closed EOW brane as a discrete series character, we use the group theory framework as a guide towards formulating the analogous supersymmetric problem. We compute these amplitudes explicitly in the supersymmetric generalizations of JT gravity ($\mathcal{N}=1,2,4$), motivated by the prospective of possibly finite amplitudes. In the process, we develop some of the representation theory of OSp$(2\vert 2,\mathbb{R})$ and PSU($1,1\vert 2)$, relevant for the $\mathcal{N}=2$ and $\mathcal{N}=4$ cases.