Supermembrane interaction with dynamical D=4 N=1 supergravity. Superfield Lagrangian description and spacetime equations of motion

TL;DR

This paper derives the complete equations of motion for a supermembrane interacting with dynamical D=4 N=1 supergravity using superfield formalism, revealing effects on the cosmological constant across spacetime regions separated by the supermembrane.

Contribution

It provides a full superfield Lagrangian formulation and analyzes the impact on the cosmological constant in the context of supermembrane-supergravity interactions.

Findings

Cosmological constant varies across spacetime regions separated by the supermembrane.

Superfield equations are solved explicitly for auxiliary fields.

Dynamical effects lead to different cosmological constants in different spacetime branches.

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 gauge where the supermembrane Goldstone field is set to zero. 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.