On Domain Walls of N=1 Supersymmetric Yang-Mills in Four Dimensions

TL;DR

This paper investigates BPS domain walls in N=1 supersymmetric Yang-Mills theory across various gauge groups, revealing their degeneracies and connections to D-branes and dualities, with specific focus on SU(N) cases.

Contribution

It provides a detailed analysis of domain wall degeneracies and their relation to D-branes and large N duality in supersymmetric Yang-Mills theories.

Findings

Degeneracies of domain walls are characterized for arbitrary gauge groups.

For SU(N), domain walls correspond to wrapped D-branes with a 2+1D U(k) gauge theory.

Counting of BPS degeneracies matches theoretical expectations.

Abstract

We study the BPS domain walls of supersymmetric Yang-Mills for arbitrary gauge group. We describe the degeneracies of domain walls interpolating between arbitrary pairs of vacua. A recently proposed large N duality sheds light on various aspects of such domain walls. In particular, for the case of G = SU(N) the domain walls correspond to wrapped D-branes giving rise to a 2+1 dimensional U(k) gauge theory on the domain wall with a Chern-Simons term of level N. This leads to a counting of BPS degeneracies of domain walls in agreement with expected results.