Hidden Role of Maxwell Superalgebras in the Free Differential Algebras of D=4 and D=11 Supergravity

TL;DR

This paper reveals that Maxwell superalgebras serve as hidden superalgebras underlying D=4 and D=11 supergravity, providing a new algebraic framework for understanding their Free Differential Algebras and gauge structures.

Contribution

It demonstrates the role of Maxwell superalgebras as hidden structures underlying supergravity theories in four and eleven dimensions, extending the algebraic understanding of these models.

Findings

Maxwell superalgebra underlies D=4 supergravity with a 2-form gauge potential.

Super-Maxwell algebra is fundamental for D=11 supergravity's Free Differential Algebra.

Extra spinors are crucial for reproducing supergravity Free Differential Algebras on superspace.

Abstract

The purpose of this paper is to show that the so-called Maxwell superalgebra in four dimensions, which naturally involves the presence of a nilpotent fermionic generator, can be interpreted as a hidden superalgebra underlying N = 1, D=4 supergravity extended to include a 2-form gauge potential associated to a 2-index antisymmetric tensor. In this scenario, the theory is appropriately discussed in the context of Free Differential Algebras (an extension of the Maurer-Cartan equations to involve higher-degree differential forms). The study is then extended to the Free Differential Algebra describing D=11 supergravity, showing that, also in this case, there exists a super-Maxwell algebra underlying the theory. The same extra spinors dual to the nilpotent fermionic generators whose presence is crucial for writing a supersymmetric extension of the Maxwell algebras, both in the D=4 and in the D=11 case, turn out to be fundamental ingredients also to reproduce the D=4 and D=11 Free Differential Algebras on ordinary superspace, whose basis is given by the supervielbein. The analysis of the gauge structure of the supersymmetric Free Differential Algebras is carried on taking into account the gauge transformations from the hidden supergroup-manifold associated with the Maxwell superalgebras.