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

Understand

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.