Domain walls in supersymmetric Yang-Mills theories

We study BPS-saturated domain walls in the supersymmetric SU(2) gauge theor y. For a theory with a very light adjoint scalar (mass m less than or simil ar to Lambda/400) we use the perturbed N = 2 Seiberg-Witten theory to calcu late the actual field configuration of the domain wall. The wall has a sand wich-like five-layer structure of three distinct phases - electric confinem ent, Coulomb and oblique confinement-separated by two separate transition r egions. 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 con densate show up in the same region of space, a phenomenon indescribable in terms of a local field theory. Nevertheless, we argue that the BPS-saturate d domain wall continues to exist in this regime and give a qualitative desc ription of the scalar and gaugino condensates, Finally, we discuss the doma in walls in MQCD and translate the BPS conditions into coupled non-linear d ifferential equations. (C) 1999 Elsevier Science B.V. All rights reserved.