Brane dynamics and 3D Seiberg duality on the domain walls of 4D N=1 SYM

We study a three-dimensional U(k) Yang-Mills Chern-Simons theory with adjoint matter preserving two supersymmetries. According to Acharya and Vafa, this theory describes the low-energy worldvolume dynamics of BPS domain walls in four-dimensional N = 1 SYM theory. We demonstrate how to obtain the same theory in a brane configuration of type IIB string theory that contains threebranes and fivebranes. A combination of string and field theory techniques allows us to re-formulate some of the well-known properties of N = 1 SYM domain walls in a geometric language and to postulate a Seiberg-like duality for the Acharya-Vafa theory. In the process, we obtain new information about the dynamics of branes in setups that preserve two supersymmetries. Using similar methods we also study other N = 1 CS theories with extra matter in the adjoint and fundamental representations of the gauge group.