Domain walls in supersymmetric Yang-Mills theories

Abstract

We study BPS-saturated domain walls in the supersymmetric SU(2) gauge theory. For a theory with a very light adjoint scalar (mass m ≲ Λ/400) we use the perturbed N = 2 Seiberg-Witten theory to calculate the actual field configuration of the domain wall. The wall has a sandwich-like five-layer structure of three distinct phases—electric confinement, Coulomb and oblique confinement—separated by two separate transition regions. For larger scalar masses, the three-phase structure disappears and the Seiberg-Witten theory becomes inadequate because of two major problems: First, the higher-derivative interactions between the light fields become relevant and second, both the magnetic monopole condensate and the dyon condensate show up in the same region of space, a phenomenon indescribable in terms of a local field theory. Nevertheless, we argue that the BPS-saturated domain wall continues to exist in this regime and give a qualitative description of the scalar and gaugino condensates. Finally, we discuss the domain walls in MQCD and translate the BPS conditions into coupled non-linear differential equations.