BPS-Saturated Walls in Supersymmetric Theories

TL;DR

This paper investigates BPS-saturated domain walls in four-dimensional supersymmetric theories, establishing criteria for partial supersymmetry preservation, deriving central charges in various models, and introducing the creek equations related to these solutions.

Contribution

It provides new criteria linking supersymmetry preservation to central extensions and introduces the creek equations for BPS domain walls in supersymmetric theories.

Findings

Criteria relating supersymmetry preservation to central charges

Explicit derivation of central charges in multiple models

Introduction of the creek equations for BPS domain walls

Abstract

Domain-wall solutions in four-dimensional supersymmetric field theories with distinct discrete vacuum states lead to the spontaneous breaking of supersymmetry, either completely or partially. We consider in detail 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 central 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 generalized 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 analog high-viscosity fluid on a profile which is given by the superpotential of the original problem. Some possible applications are considered.