Non-Abelian Vortices without Dynamical Abelianization

TL;DR

This paper identifies non-Abelian vortices in softly-broken ${ m N}=2$ SQCD that retain their non-Abelian flux moduli without reducing to Abelian vortices, revealing their semi-classical origin and connection to non-Abelian monopoles.

Contribution

It demonstrates the existence of non-Abelian vortices with stable flux moduli in specific vacua of ${ m N}=2$ SQCD, and explains their semi-classical origin and behavior.

Findings

Non-Abelian vortices with flux moduli $CP^{n-1} imes CP^{r-1}$ identified.

For $n>r$, SU(n) fluctuations become strongly coupled and Abelianize.

The vortices' properties relate to the semi-classical origin of non-Abelian monopoles.

Abstract

Vortices carrying truly non-Abelian flux moduli, which do not dynamically reduce to Abelian vortices, are found in the context of softly-broken ${\cal N}=2$ supersymmetric chromodynamics (SQCD). By tuning the bare quark masses appropriately we identify the vacuum in which the underlying SU(N) gauge group is partially broken to $SU(n) \times SU(r) \times U(1)/{\mathbbm Z}_{K}$, where $K$ is the least common multiple of $(n, r)$, and with $N_{f}^{su(n)}=n$ and $N_{f}^{su(r)}=r$ flavors of light quark multiplets. At much lower energies the gauge group is broken completely by the squark VEVs, and vortices develop which carry non-Abelian flux moduli $CP^{n-1}\times CP^{r-1}$. For $n>r$ we argue that the SU(n) fluctuations become strongly coupled and Abelianize, while leaving weakly fluctuating $SU(r)$ flux moduli. This allows us to recognize the semi-classical origin of the light non-Abelian monopoles found earlier in the fully quantum-mechanical treatment of 4D SQCD.