Non-Abelian Vortices without Dynamical Abelianization

Abstract

Vortices carrying truly non-Abelian flux moduli, which do not dynamically reduce to Abelian vortices, are found in the context of softly-broken $\mathcal{N}=2$ 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 $C{P}^{n-1}\times C{P}^{r-1}$. 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.

22 pages, 4 figures, One section (Section 2) added, and an extended discussion added in Section 5

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• Fractional Vortices and Lumps
• Vortices and Monopoles in Mass-deformed SO and USp Gauge Theories
• SO and USp Kahler and Hyper-Kahler Quotients and Lumps
• Non-Abelian Duality and Confinement in N=2 Supersymmetric QCD
• Group Theory of Non-Abelian Vortices
• On the Stability of Non-Abelian Semi-local Vortices
• Non-Abelian monopole-vortex complex
• Crossover between Abelian and non-Abelian confinement in N=2 supersymmetric QCD
• Zero-modes of Non-Abelian Solitons in Three Dimensional Gauge Theories