Matter-coupled de Sitter Supergravity

TL;DR

This paper develops a comprehensive framework for constructing de Sitter supergravity models coupled with matter multiplets, highlighting the role of nilpotent multiplets and providing explicit actions and conditions for de Sitter vacua.

Contribution

It generalizes the construction rules for pure de Sitter supergravity to include matter multiplets and provides a complete explicit action with conditions for de Sitter vacua.

Findings

Derived the full supergravity action with matter and nilpotent multiplets.

Identified the potential and conditions for de Sitter vacua.

Presented explicit unitary gauge action.

Abstract

De Sitter supergravity describes interaction of supergravity with general chiral and vector multiplets as well as one nilpotent chiral multiplet. The extra universal positive term in the potential due to the nilpotent multiplet, corresponding to the anti-D3 brane in string theory, supports de Sitter vacua in these supergravity models. In the flat space limit these supergravity models include the Volkov-Akulov model with a non-linearly realized supersymmetry. The rules for constructing pure de Sitter supergravity action are generalized here in presence of other matter multiplets. We present a strategy to derive the complete closed form general supergravity action with a given Kahler potential $K$, superpotential $W$ and vector matrix $f_{AB}$ interacting with a nilpotent chiral multiplet. It has the potential $V=e^K(|F^2 |+ |DW|^2 - 3 |W|^2)$, where $F$ is a necessarily non-vanishing value of the auxiliary field of the nilpotent multiplet. De Sitter vacua are present under simple condition that $|F^2|- 3|W|^2>0$. A complete explicit action in the unitary gauge is presented.