Supermembranes and domain walls in \(\mathcal N=1\), \(D=4\) SYM

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.