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

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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.
© The Authors. We are very much indebted to E. Alvarez for countless discussions on unimodular supergravity and for guidance. We thank T. Ortin for provinding us with information relevant to this paper. This work has received funding from the Spanish Research Agency (Agencia Estatal de Investigacion) through the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597, and the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grants agreement No 674896 and No 690575. We also have been partially supported by FPA2016-78645-P(Spain). RSG is supported by the Spanish FPU Grant No FPU16/01595. CPM has been partially supported by the Spanish Ministerio de Ciencia, Innovacion y Universidades through grant PGC2018-095382-B-I00. We thank an anonymous referee for her/his comments and suggestions.
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