De Sitter Supergravity Model Building

TL;DR

This paper derives an explicit de Sitter supergravity action incorporating multiple matter multiplets and a nilpotent multiplet, with a universal formula for fermionic interactions, enabling advanced model building in supergravity.

Contribution

It provides a comprehensive, explicit form of de Sitter supergravity action with a nilpotent multiplet, including a universal expression for fermionic terms, advancing supergravity model construction.

Findings

Explicit supergravity action with nilpotent multiplet derived

Universal closed form for fermionic interactions provided

Action applicable to arbitrary matter couplings in supergravity

Abstract

We present the explicit de Sitter supergravity action describing the interaction of supergravity with an arbitrary number of chiral and vector multiplets as well as one nilpotent chiral multiplet. The action has a non-Gaussian dependence on the auxiliary field of the nilpotent multiplet, however, it can be integrated out for an arbitrary matter-coupled supergravity. The general supergravity action with a given Kahler potential $K$, superpotential $W$ and vector matrix $f_{AB}$ interacting with a nilpotent chiral multiplet consists of the standard supergravity action defined by $K$, $W$ and $f_{AB}$ where the scalar in the nilpotent multiplet has to be replaced by a bilinear combination of the fermion in the nilpotent multiplet divided by the Gaussian value of the auxiliary field. All additional contributions to the action start with terms quartic and higher order in the fermion of the nilpotent multiplet. These are given by a simple universal closed form expression.