Three form potential in (special) minimal supergravity superspace and supermembrane supercurrent

Abstract

This contribution begins the study of the complete superfield Lagrangian description of the interacting system of D=4 N=1 supergravity (SUGRA) and supermembrane. Firstly, we review a 'three form supergravity' by Ovrut and Waldram, which we prefer to call 'special minimal supergravity'. This off-shell formulation of simple SUGRA is appropriate for our purposes as the supermembrane action contains the so-called Wess-Zumino term given by the integral over a three form potential in superspace, C3. We describe this formulation in the frame of Wess--Zumino superfield approach, showing how the basic variations of minimal SUGRA are restricted by the conditions of the existence of a three-form potential C3 in its superspace. In this language the effect of dynamical generation of cosmological constant, known to be characteristic for this formulation of SUGRA, appears in its superfield form, first described by Ogievetsky and Sokatchev in their formulation of SUGRA as a theory of axial vector superfield. Secondly, we vary the supermembrane action with respect to the special minimal SUGRA superfields (basic variations) and obtain the supercurrent superfields as well as the supergravity superfield equations with the supermembrane contributions.

18 pages, no figures. V2: Important references added. The abstract and presentation have been changed to reflect the overloop with that. Submitted to the QTS7 Proceedings. J. Phys. style used

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• An Axion-induced SM/MSSM Higgs Landscape and the Weak Gravity Conjecture
• Three-forms, dualities and membranes in four-dimensional supergravity
• Scanning of the Supersymmetry Breaking Scale and the Gravitino Mass in Supergravity
• Liberated N=1 Supergravity
• Supermembrane interaction with dynamical D=4 N=1 supergravity. Superfield Lagrangian description and spacetime equations of motion
• On the dynamical origin of parameters in $\mathcal{N}=2$ Supersymmetry
• 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
• Superstring at the boundary of open supermembrane interacting with D=4 supergravity and matter supermultiplets