From Linear to Non-linear Supersymmetry via Functional Integration

TL;DR

This paper derives a pure de Sitter supergravity action with non-linear supersymmetry from linear models using functional integration, demonstrating the universality of the resulting action for various matter couplings.

Contribution

It introduces a method to obtain non-linear supersymmetric actions from linear models via non-Gaussian functional integration, extending the understanding of de Sitter supergravity.

Findings

Derived explicit pure de Sitter supergravity actions.

Showed the universality of the action formula for matter couplings.

Provided examples illustrating the method's application.

Abstract

We derive a complete pure de Sitter supergravity action with non-linearly realized supersymmetry and its rigid limit, the Volkov-Akulov action, from the corresponding models with linear supersymmetry, by computing the path integral in the limit of infinite sgoldstino mass. In this, we use a non-Gaussian functional integration formula that was recently discovered in a derivation of de Sitter supergravity from the superconformal theory. We also present explicit examples of pure dS supergravity and the case with one matter multiplet. These two simple examples serve as a test and a demo of the universal action formula valid for de Sitter supergravities with general matter coupling.