Unimodular vs Nilpotent Superfield Approach to Pure dS Supergravity

TL;DR

This paper compares different supergravity approaches to constructing de Sitter vacua, revealing their equivalence up to cubic order and suggesting a broader framework for deriving de Sitter spacetimes from fundamental theories.

Contribution

It establishes a connection between unimodular supergravity, nilpotent superfields, and goldstino brane approaches, unifying them within a potential general framework.

Findings

Actions match up to cubic order after field redefinitions.

Different approaches to de Sitter supergravity are shown to be equivalent.

Suggests a more general framework for deriving de Sitter spacetimes.

Abstract

Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-St\"uckelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.