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.

We present the superfield action for the dynamical N = 1 D = 4 supermembrane in interaction with a dynamical scalar multiplet and use it to derive the superfield equations of motion. These include the supermembrane equations, which formally coincide with equations of supermembrane in a background of the (off-shell) scalar multiplet, and the special chiral superfield equations with supermembrane source. In the case when the scalar supermultiplet part of the action contains only the simplest kinetic term we have also extracted the spacetime component field equations from the superfield equations and solve these in the leading order on supermembrane tension. The inclusion of nontrivial superpotential and relation with known supersymmetric domain wall solutions is briefly discussed.

Abstract:We obtain the complete set of equations of motion for the interacting system of supermembrane and dynamical D = 4 N = 1 supergravity by varying its complete superfield action and writing the resulting superfield equations in the special "WZθ =0 " gauge where the supermembrane Goldstone field is set to zero (θ = 0). We solve the equations for auxiliary fields and discuss the effect of dynamical generation of cosmological constant in the Einstein equation of interacting system and its renormalization due to some regular contributions from supermembrane. These two effects (discussed in late 70th and 80th, in the bosonic perspective and in the supergravity literature) result in that, generically, the cosmological constant has different values in the branches of the spacetime separated by the supermembrane worldvolume.

We study the properties of the covariant supersymmetric and -symmetric action for a system of N nearly coincident M0-branes (mM0 system) in flat 11-dimensional (11D) superspace and obtain supersymmetric equations for this dynamical system. Although a single M0-brane is the massless 11D superparticle, center-of-energy motion of the mM0 system is characterized by a non-negative constant mass M constructed from the matrix fields describing the relative motion of mM0 constituents. We show that a bosonic solution of the mM0 equations can be supersymmetric iff this effective mass vanishes, M 2 ¼ 0, and that all the supersymmetric bosonic solutions preserve just one half of the 11D supersymmetry.

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.