Supergravity Actions with Integral Forms

TL;DR

This paper introduces integral forms as a robust mathematical framework for constructing supergravity actions, clarifying their geometric foundations, and proving a key theorem linking superfield and component actions.

Contribution

It reformulates supergravity's geometric approach using integral forms and provides a proof of Gates' Ectoplasmic Integration Theorem.

Findings

Integral forms enable consistent integration on supermanifolds.

The reformulation clarifies the group geometrical approach to supergravity.

A proof of Gates' Ectoplasmic Integration Theorem is provided.

Abstract

Integral forms provide a natural and powerful tool for the construction of supergravity actions. They are generalizations of usual differential forms and are needed for a consistent theory of integration on supermanifolds. The group geometrical approach to supergravity and its variational principle are reformulated and clarified in this language. Central in our analysis is the Poincare' dual of a bosonic manifold embedded into a supermanifold. Finally, using integral forms we provide a proof of Gates' so-called "Ectoplasmic Integration Theorem", relating superfield actions to component actions.