The Integral Form of Supergravity

TL;DR

This paper derives the superspace action of D=3, N=1 supergravity using integral forms on supermanifolds, demonstrating the equivalence between superspace and component actions through a group geometrical approach.

Contribution

It introduces a novel integral form method for deriving supergravity actions and connects superspace and component formulations via target space picture changing operators.

Findings

Derived superspace supergravity action as an integral on supermanifold

Showed the equivalence between superspace and component actions

Provided a geometric interpretation using group manifold approach

Abstract

By using integral forms we derive the superspace action of D=3, N=1 supergravity as an integral on a supermanifold. The construction is based on target space picture changing operators, here playing the role of Poincare' duals to the lower-dimensional spacetime surfaces embedded into the supermanifold. We show how the group geometrical action based on the group manifold approach interpolates between the superspace and the component supergravity actions, thus providing another proof of their equivalence.