# Non-Abelian strings in N=1 supersymmetric QCD

## TL;DR

This paper investigates non-Abelian strings in N=1 supersymmetric QCD, deriving an effective world sheet theory, analyzing fermionic zero modes, and exploring the impact of deformation from N=2 to N=1 supersymmetry.

## Contribution

It provides a detailed analysis of non-Abelian strings in N=1 SQCD, including the effective CP(N-1) model and the lifting of fermionic zero modes due to deformation.

## Key findings

- The effective world sheet theory remains a CP(N-1) model with an exponentially small scale.
- Fermionic superorientational zero modes are lifted in the N=1 limit.
- Non-Abelian strings are no longer BPS after deformation.

## Abstract

Non-Abelian flux tubes (strings) are well studied in N=2 supersymmetric QCD in (3+1) dimensions. In addition to translational zero modes they have also orientational moduli associated with rotations of their fluxes inside a non-Abelian group. The dynamics of the orientational moduli is described by the two dimensional CP(N-1) model living on the world sheet of the non-Abelian string. In this paper we consider a deformation of N=2 supersymmetric QCD with the U(N) gauge group and N_f=N quark flavors with a mass term $\mu$ of the adjoint matter. In the limit of large $\mu$ the theory flows to an N=1 supersymmetric QCD. We study the solution for the non-Abelian string in this limit and derive an effective theory on the string world sheet. The bosonic sector of this theory is still given by the CP(N-1) model but its scale is exponentially small as compared to the scale of the four dimensional bulk theory in contrast to the N=2 case where these scales are equal. We study also the fermionic sector of the world sheet theory. Upon the deformation the non-Abelian string is no longer BPS and we show that the fermionic superorientational zero modes are all lifted. This leaves us with the pure bosonic CP(N-1) model on the string world sheet in the limit of N=1 QCD. We also discuss what happens to confined monopoles at large $\mu$.