On the Hidden Maxwell Superalgebra underlying \(D=4\) Supergravity

Abstract

In this work, we expand the hidden \(AdS\)-Lorentz superalgebra underlying \(D=4\) supergravity, reaching a (hidden) Maxwell superalgebra. The latter can be viewed as an extension involving cosmological constant of the superalgebra underlying \(D=4\) supergravity in flat space. We write the Maurer-Cartan equations in this context and we find some interesting extensions of the parametrization of the \(3\)-form \(A^{(3)}\), which appears in the Free Differential Algebra in Minkowski space, in terms of \(1\)-forms. We find out that the structure of these extensions of the parametrization of \(A^{(3)}\), and consequently the structure of the corresponding boundary contribution \(dA^{(3)}\), strongly depends on the form of the extra fermionic generator appearing in the hidden Maxwell superalgebra.