On supermembrane supercurrent and special minimal supergravity

Abstract

In this contribution we review recent progress in studying the superfield Lagrangian description of the interacting system of D = 4 𝒩 = 1 supergravity (SUGRA) and supermembrane in the frame of Wess–Zumino superfield approach. The off-shell formulation of simple SUGRA by Ovrut and Waldram, which we prefer to call `special minimal supergravity', is appropriate for this purpose. We discuss the superfield form of this formulation, 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. We also describe the effect of dynamical generation of cosmological constant, known to be characteristic for this formulation of SUGRA, in its superfield form, and notice that the same effect had been found by Ogievetsky and Sokatchev in their formulation of SUGRA as a theory of axial vector superfield. 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.