Counting Domain Walls in N=1 Super Yang-Mills Theory

TL;DR

This paper investigates the number of BPS domain walls in N=1 super Yang-Mills theory by analyzing a weakly coupled Higgs phase and using the Witten index, confirming results with string theory methods.

Contribution

It introduces a method to count domain walls via the Witten index in a Higgs phase, connecting gauge theory and string theory realizations.

Findings

Number of domain walls matches string theory predictions

Witten index remains invariant under deformation to Higgs phase

Worldvolume sigma model has Grassmannian target space

Abstract

We study the multiplicity of BPS domain walls in N=1 super Yang-Mills theory, by passing to a weakly coupled Higgs phase through the addition of fundamental matter. The number of domain walls connecting two specified vacuum states is then determined via the Witten index of the induced worldvolume theory, which is invariant under the deformation to the Higgs phase. The worldvolume theory is a sigma model with a Grassmanian target space which arises as the coset associated with the global symmetries broken by the wall solution. Imposing a suitable infrared regulator, the result is found to agree with recent work of Acharya and Vafa in which the walls were realized as wrapped D4-branes in IIA string theory.