Super Yang-Mills Theory with Impurity Walls and Instanton Moduli Spaces

TL;DR

This paper studies a supersymmetric Yang-Mills theory with impurity walls, revealing that its Higgs branch corresponds to instanton moduli spaces on multi-Taub-NUT space, and explores dualities and metric computations.

Contribution

It identifies the Higgs branch of the theory with bow equations for instantons and analyzes duality transformations and metric properties of the moduli space.

Findings

Higgs branch matches bow equations for instantons on multi-Taub-NUT space.

Electric-magnetic duality swaps impurity wall types while preserving the bulk theory.

One-loop calculations yield the asymptotic metric on the Higgs branch.

Abstract

We explore maximally supersymmetric Yang-Mills theory with walls of impurities respecting half of the supersymmetries. The walls carry fundamental or bifundamental matter multiplets. We employ three-dimensional N=2 superspace language to identify the Higgs branch of this theory. We find that the vacuum conditions determining the Higgs branch are exactly the bow equations yielding Yang-Mills instantons on a multi-Taub-NUT space. Under electric-magnetic duality, the super Yang-Mills theory describing the bulk is mapped to itself, while the fundamental- and bifundamental-carrying impurity walls are interchanged. We perform a one-loop computation on the Coulomb branch of the dual theory to find the asymptotic metric on the original Higgs branch.