Complex three-form supergravity and membranes

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.

22 pages

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• Three-forms, Supersymmetry and String Compactifications
• Higher derivative three-form gauge theories and their supersymmetric extension
• On the dynamical origin of parameters in $\mathcal{N}=2$ Supersymmetry
• Off-shell unimodular N=1, d=4 supergravity
• Topological couplings in higher derivative extensions of supersymmetric three-form gauge theories
• Higher Forms and Membranes in 4D Supergravities
• Three-forms and Fayet-Iliopoulos terms in Supergravity: Scanning Planck mass and BPS domain walls
• Supermembranes and domain walls in $\mathcal{N}=1$, $D=4$ SYM
• de Sitter decay through goldstino evaporation
• Nilpotent $\mathcal{N}=1$ tensor multiplet
• Superstring at the boundary of open supermembrane interacting with D=4 supergravity and matter supermultiplets
• On the role of torsion and higher forms in off-shell supergravity