Non-Abelian vortices with product moduli

Abstract

Vortices of a new type, carrying non-Abelian flux moduli $C{P}^{n\ensuremath{-}1}\ifmmode\times\else\texttimes\fi{}C{P}^{r\ensuremath{-}1}$, are found in the context of softly broken $\mathcal{N}=2$ supersymmetric quantum chromodynamics. By tuning the bare quark masses appropriately, we identify the vacuum in which the underlying $SU(N)$ gauge group is partially broken to $SU(n)\ifmmode\times\else\texttimes\fi{}SU(r)\ifmmode\times\else\texttimes\fi{}U(1)/{\mathbb{Z}}_{K}$, 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 vacuum expectation values, and vortices develop which carry non-Abelian flux moduli $C{P}^{n\ensuremath{-}1}\ifmmode\times\else\texttimes\fi{}C{P}^{r\ensuremath{-}1}$. For $n>r$, at the length scale at which the $SU(n)$ fluctuations become strongly coupled and Abelianize, the vortex still carries weakly fluctuating $SU(r)$ flux moduli. We discuss the possibility that these vortices are related to the light non-Abelian monopoles found earlier in the fully quantum-mechanical treatment of $4D$ supersymmetric quantum chromodynamics.