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

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 Gold-stone 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 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.