Supergravity as a constrained BF theory

TL;DR

This paper formulates ${\cal N}=1$ supergravity as a constrained BF theory with $OSp(4|1)$ gauge superalgebra, introducing terms involving the Immirzi parameter that could influence quantum properties.

Contribution

It presents a novel formulation of supergravity as a constrained BF theory incorporating the Immirzi parameter, linking classical and quantum aspects.

Findings

Derives a modified supergravity Lagrangian with Immirzi parameter terms.

Shows these terms do not alter classical equations but may impact quantum theory.

Discusses perturbation theory around the supersymmetric topological vacuum.

Abstract

In this paper we formulate ${\cal N}=1$ supergravity as a constrained $BF$ theory with $OSp(4|1)$ gauge superalgebra. We derive the modified supergravity Lagrangian that, apart from the standard supergravity with negative cosmological constant, contains terms proportional to the (inverse of) Immirzi parameter. Although these terms do not change classical field equations, they might be relevant in quantum theory. We briefly discuss the perturbation theory around the supersymmetric topological vacuum.