BPS-SATURATED WALLS IN SUPERSYMMETRIC THEORIES

Domain-wall solutions in four-dimensional supersymmetric field theorie s with distinct discrete vacuum states lead to the spontaneous breakin g of supersymmetry, either completely or partially. We consider in det ail the case when the domain walls are the BPS-saturated states, and 1 /2 of supersymmetry is preserved. Several useful criteria that relate the preservation of 1/2 of supersymmetry on the domain walls to the ce ntral extension appearing in the N=1 superalgebras are established. We explain how the central extension can appear in N=1 supersymmetry and explicitly obtain the central charge in various models: the generaliz ed Wess-Zumino models, and supersymmetric Yang-Mills theories with or without matter. The BPS-saturated domain walls satisfy the first-order differential equations which we call the creek equations, since they formally coincide with the (complexified) equations of motion of an an alog high-viscosity fluid on a profile which is given by the superpote ntial of the original problem. Some possible applications are consider ed. We also briefly discuss BPS-saturated strings. [S0556-2821(97)0322 4-4].