# Supermembranes and domain walls in $\mathcal N=1$, $D=4$ SYM

## TL;DR

This paper develops a supersymmetric membrane action coupled to $
abla=1$, $D=4$ super-Yang-Mills theory, revealing its role in domain walls, vacua separation, and BPS solutions within the Veneziano-Yankielowicz framework.

## Contribution

It introduces a new supersymmetric membrane model coupled to $
abla=1$, $D=4$ SYM, elucidating its effects on vacua, domain walls, and BPS solutions.

## Key findings

- Membrane sources modify VY equations and vacua.
- Explicit BPS domain-wall solutions are constructed.
- Membrane coupling accounts for domain-wall tension.

## Abstract

We construct a manifestly supersymmetric and kappa-symmetry invariant worldvolume action describing the coupling of a dynamical membrane to an $\mathcal N=1$, $D=4$ $SU(N)$ super-Yang-Mills multiplet. Worldvolume scalar fields in this action are a Goldstone and a Goldstino associated with spontaneous breaking, by the membrane, of half of $\mathcal N=1$, $D=4$ supersymmetry. When the Goldstone fields are set to zero, the model reduces to an $\mathcal N=1$, $d=3$ $SU(N)$ Chern-Simons theory induced by the SYM coupling. We show that, when the membrane couples to the Veneziano-Yankielowicz (VY) effective theory of the $\mathcal N=1$ SYM, it sources VY bulk field equations, separates two distinct SYM vacua and provides the missing contribution to the tension of BPS saturated domain-wall configurations, for which the membrane serves as a core. As a result, we obtain explicit BPS domain-wall solutions in the Veneziano-Yankielowicz theory. We also briefly discuss a supersymmetric system of an open membrane having a string attached to its boundary and coupled to a massive extension of the Veneziano-Yankielowicz model.