Abstract
There exist two variants of the old minimal formulation for \( \mathcal{N} \) = 1 supergravity in four dimensions, in which one or each of the two auxiliary scalars is replaced by the field strength of a gauge three-form. These theories are known as three-form supergravity and complex three-form supergravity, respectively. For each of them, we present a super-Weyl invariant coupling of supergravity to the supermembrane and prove kappa-invariance of the resulting action. In the case of three-form supergravity, we demonstrate that the action constructed reduces to that given by Ovrut and Waldram twenty years ago upon imposing a super-Weyl gauge in which the compensating three-form superfield is set to a constant.
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Kuzenko, S.M., Tartaglino-Mazzucchelli, G. Complex three-form supergravity and membranes. J. High Energ. Phys. 2017, 5 (2017). https://doi.org/10.1007/JHEP12(2017)005
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DOI: https://doi.org/10.1007/JHEP12(2017)005