Domain Walls in Supersymmetric Yang-Mills Theories

TL;DR

This paper investigates the structure and properties of BPS domain walls in supersymmetric SU(2) gauge theories, revealing a layered phase structure for light scalars and discussing the persistence of these walls at larger masses.

Contribution

It provides a detailed calculation of domain wall configurations using perturbed N=2 Seiberg-Witten theory and explores their behavior beyond the regime where the theory is fully applicable.

Findings

Layered five-phase structure of domain walls for light scalars

Disappearance of phase structure at larger scalar masses

Qualitative description of condensates in the non-ideal regime

Abstract

We study BPS saturated domain walls in the supersymmetric SU(2) gauge theory. For a theory with a very light adjoint scalar (mass <~ Lambda/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.