Super-Poincare' algebras, space-times and supergravities (II)

TL;DR

This paper reformulates supergravity theories using supermanifold theory, demonstrating the equivalence of 11D-supergravity equations to covariant equations on supermanifolds, thus providing a geometric perspective.

Contribution

It introduces a supermanifold framework for supergravity, connecting traditional equations to a covariant geometric formulation.

Findings

Supergravity theories are expressed in supermanifold language.

11D-supergravity equations are shown to be covariant on supermanifolds.

The geometric formulation aligns with previous algebraic approaches.

Abstract

The presentation of supergravity theories of our previous paper "Super-Poincare' algebras, space-times and supergravities (I)" is re-formulated in the language of Berezin-Leites-Kostant theory of supermanifolds. It is also shown that the equations of Cremmer, Julia and Scherk's theory of 11D-supergravity are equivalent to manifestly covariant equations on a supermanifold.