Degenerate Domain Walls in Supersymmetric Theories

TL;DR

This paper investigates the properties and classification of degenerate domain walls in supersymmetric theories, revealing their multiplicities, types, and unique junction phenomena in supersymmetric QCD.

Contribution

It classifies degenerate domain walls in supersymmetric QCD, proving their multiplicity formula and identifying two classes with distinct local and topological features.

Findings

Derived the multiplicity formula for domain walls as a combinatorial index.

Identified two classes of degenerate domain walls: locally distinguishable and topologically differentiated.

Discovered two-wall junctions unique to supersymmetric theories with central extensions.

Abstract

In supersymmetric Yang-Mills theories (SYM) tension-degenerate domain walls are typical. Adding matter fields in fundamental representation we arrive at supersymmetric QCD (SQCD) supporting similar walls. We demonstrate that the degenerate domain walls can belong to one of two classes: (i) locally distinguishable, i.e. those which differ from each other locally (which could be detected in local measurements); and (ii) those which have identical local structure and are differentiated only topologically, through a judicially chosen compactification of $\mathbb{R}^4$. Depending on the number of flavors $F$ and the pattern of Higgsing both classes can coexists among SQCD $k$ walls interpolating between the vacua $n$ and $n+k$. We prove that the overall multiplicity of the domain walls obtained after accounting for both classes is $\nu_{N,k}^\text{walls}= N!/\big[(N-k)!k!\big]$, as was discovered previously in limiting cases. (Here $N$ is the number of colors.) Thus, $\nu_{N,k}^\text{walls}$ is a peculiar index. For the locally distinguishable degenerate domain walls we observe two-wall junctions, a phenomenon specific for supersymmetry with central extensions. This phenomenon does not exist for topological replicas.