What Becomes of Semilocal non-Abelian Strings in ${\mathcal N}=1$ Supersymmetric QCD

TL;DR

This paper investigates how non-Abelian vortex strings in supersymmetric QCD evolve as the theory transitions from ${ m N}=2$ to ${ m N}=1$ supersymmetry, focusing on the behavior of size moduli and their impact on the effective string theory.

Contribution

It demonstrates that in the large deformation limit, size moduli are suppressed, reducing the effective string theory to the well-known $CP(N-1)$ model, clarifying the fate of semilocal strings in ${ m N}=1$ QCD.

Findings

Size moduli develop a potential that shrinks the string's transverse size.

In the large $$ limit, size moduli decouple from the effective theory.

The effective theory on the string reduces to the $CP(N-1)$ model.

Abstract

We study non-Abelian vortex strings in ${\mathcal N}=2$ supersymmetric QCD with the gauge group U$(N)$ deformed by the mass $\mu$ of the adjoint matter. This deformation breaks ${\mathcal N}=2$ supersymmetry down to ${\mathcal N}=1$ and in the limit of large $\mu$ the theory flows to ${\mathcal N}=1$ QCD. Non-Abelian strings in addition to translational zero modes have orientation moduli. In the ${\mathcal N}=2$ limit of small $\mu$ the dynamics of orientational moduli is described by the two dimensional $CP(N-1)$ model for QCD with $N_f=N$ flavors of quark hypermultiplets. For the case of $N_f>N$ the non-Abelian string becomes semilocal developing additional size moduli which modify the effective two dimensional $\sigma$-model on the string making its target space non-compact. In this paper we consider the $\mu$-deformed theory with $N_f>N$ eventually making $\mu$ large. We show that size moduli develop a potential that forces the string transverse size to shrink. Eventually in the large $\mu$ limit size moduli decouple and the effective theory on the string reduces to the $CP(N-1)$ model. We also comment on physics of confined monopoles.