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.

中文翻译：

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壳外单模 N = 1, d = 4 超重力

我们制定了一个单模 N=1, d=4 的超重力理论。我们看到定义单模超重力变换的无穷小格拉斯曼参数受到约束，并表明两个无穷小单模超重力变换的换向器接近横向微分同胚、洛伦兹变换和单模超重力变换。在此过程中，我们还表明线性化理论是引力子和引力子的超对称理论。我们看到德西特和反德西特时空是我们单模超引力理论的非超对称真空。