Gauge theory of supergravity based only on a self-dual spin connection.

Abstract

A gauge theory of supergravity is constructed based only on the supersymmetric self-dual spin connection associated to the supergroup OSp $(1|4)$. We show that Jacobson's supergravity action arises naturally from our proposed action. It is formulated by taking the self-dual part of the MacDowell-Mansouri gauge theory of supergravity. In this sense, our quadratic action in the supersymmetric self-dual curvature tensor provides a relation between these two important previous extensions of supergravity.