Abstract
We formulate a unimodular N = 1, d = 4 supergravity theory off shell. We see that the infinitesimal Grassmann parameters defining the unimodular supergravity trans- formations are constrained and show that the conmutator of two infinitesinal unimodular supergravity transformations closes on transverse diffeomorphisms, Lorentz transforma- tions 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.
Highlights
Minimal off-shell formulations of N = 1, d = 4 supergravity were formulated in [26, 27], so that the supergravity algebra closes without imposing the equations of motion of the fields
The main conclusion of this paper is that a unimodular N = 1, d = 4 Poincare supergravity can be formulated off-shell. This unimodular gravity theory is the counterpart of the standard N = 1, d = 4 Poincare supergravity
To the case of unimodular gravity, the infinitesimal parameters defining the unimodular supergravity transformations are constrained by a differential equation which make those parameters field dependent
Summary
The purpose of this paper is to formulate the minimal off-shell N = 1, d = 4 Poincare supergravity counterpart of unimodular gravity. We shall call this theory N = 1, d = 4 unimodular supergravity.
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