Superfield equations for the interacting system of D=4 N=1 supermembrane and scalar multiplet

TL;DR

This paper develops superfield equations describing the interaction of a D=4 N=1 supermembrane with a scalar multiplet, deriving both superfield and component field equations, and exploring solutions including domain walls.

Contribution

It introduces a superfield action for the interacting supermembrane and scalar multiplet, deriving equations of motion and analyzing solutions with nontrivial superpotentials.

Findings

Superfield equations for supermembrane and scalar multiplet interaction derived.

Component field equations obtained and solved at leading order.

Discussion of solutions related to supersymmetric domain walls.

Abstract

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.