Sitting on the domain walls of N=1 super Yang-Mills -: art. no. 043

In pure N = 1 supersymmetric Yang-Mills with gauge group SU( N), the domain walls which separate the N vacua have been argued, on the basis of string theory realizations, to be D-branes for the con ning string. In a certain limit, this means that a configuration of k parallel domain walls is described by a 2 + 1-dimensional U( k) gauge theory. This theory has been identified by Acharya and Vafa as the U( k) gauge theory with 4 supercharges broken by a Chern-Simons term of level N in such a way that 2 supercharges are preserved. We argue further that the gauge coupling of the domain wall gauge theory goes like g(2) similar to Lambda/N, for large N. In the case of two domain walls, we show that the U(2) world-volume theory generates a quadratic potential on the Coulomb branch at two loops in perturbation theory which is consistent with there being a supersymmetric bound state of the two wall system. A mass gap of order Lambda/N is generated around the supersymmetric minimum and we estimate the size of the bound-state to be order Lambda/root N. At large distance the potential reaches a constant that can qualitatively account for the binding energy of the two walls even though stringy effects are not, strictly speaking, decoupled.