Off-shell unimodular N=1, d=4 supergravity

TL;DR

This paper develops an off-shell formulation of unimodular N=1, d=4 supergravity, revealing its constrained transformation parameters, closure properties, and non-supersymmetric vacua like de Sitter and anti-de Sitter spaces.

Contribution

It introduces a novel off-shell unimodular supergravity framework with constrained transformation parameters and analyzes its algebraic closure and vacuum structure.

Findings

Transformation parameters are constrained in unimodular supergravity.

The algebra closes on transverse diffeomorphisms, Lorentz, and unimodular transformations.

De Sitter and anti-de Sitter spaces are non-supersymmetric vacua.

Abstract

We formulate a unimodular N=1, d=4 supergravity theory off shell. We see that the infinitesimal Grassmann parameters defining the unimodular supergravity transformations are constrained and show that the conmutator of two infinitesinal unimodular supergravity transformations closes on transverse diffeomorphisms, Lorentz transformations and unimodular supergravity transformations. Along the way, we also show that the linearized theory is a supersymmetric theory of gravitons and gravitinos. We see that de Sitter and anti-de Sitter spacetimes are non-supersymmetric vacua of our unimodular supergravity theory.