Abstract
We obtain a four-dimensional supergravity with spontaneously broken supersymmetry 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.
Highlights
The study of the general relation between linear and non-linear realizations of supersymmetry and [15, 23,24,25] for the extension of these methods to describe spontaneously broken supergravities in superspace)
We obtain a four-dimensional supergravity with spontaneously broken supersymmetry 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
Summary
When we consider the coupling of supergravity to the 3-brane as in (1.1), the 3-brane back-reacts, i.e. contributes to the supergravity equations of motion and, in particular, to those of the auxiliary fields modifying them. This trick allows us to identify the different components of the θ-expansion of EA by finding (2.15) order by order in t Another alternative procedure to arrive at recurrent relations, described in [49] (going back to [52] and [53]), uses the operator θα ∂α. Note that when the auxiliary fields are put to zero, the terms entering the second order expansions (2.19) and (2.20) coincide with the supervielbeins first constructed in [10] (see section 3). There are only linear terms in space-time derivatives of the auxiliary fields and they appear only at the quartic order. This means that in the 3-brane action (2.14) the auxiliary fields appear only linearly or quadratically and without derivatives (modulo integration by parts). As such, when the 3-brane action is coupled to the supergravity action SSG in (2.1), one can still explicitly solve the equations of motion of the auxiliary fields (2.3a) and (2.3b) modified by the presence of the goldstino fields
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