Brane induced supersymmetry breaking and de Sitter supergravity

Abstract: We obtain a four-dimensional supergravity with spontaneously broken super-symmetry allowing for de Sitter vacua by coupling a superspace action of minimal N = 1, D = 4 supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action describing the dynamics of a space-filling non-BPS 3-brane in N = 1, D = 4 superspace. To the quadratic order in the goldstino field the obtained action coincides with earlier constructions of supergravities with nilpotent superfields, while matching the higher-order contributions will require a non-linear redefinition of fields. In the unitary gauge, in which the goldstino field is set to zero, the action coincides with that of Volkov and Soroka. We also show how a nilpotency constraint on a chiral curvature superfield emerges in this formulation.