Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions

Abstract

We consider a U(2) Yang-Mills theory on M x S_F^2 where M is an arbitrary noncommutative manifold and S_F^2 is a fuzzy sphere spontaneously generated from a noncommutative U(N) Yang-Mills theory on M, coupled to a triplet of scalars in the adjoint of U(N). Employing the SU(2)-equivariant gauge field constructed in arXiv:0905.2338, we perform the dimensional reduction of the theory over the fuzzy sphere. The emergent model is a noncommutative U(1) gauge theory coupled adjointly to a set of scalar fields. We study this model on the Groenewald-Moyal plane and find that, in certain limits, it admits noncommutative, non-BPS vortex as well as flux-tube (fluxon) solutions and discuss some of their properties.

arXiv comment18+1 pages, typos corrected, published version

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• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
• Equivariant Reduction of U(4) Gauge Theory over S_F^2 x S_F^2 and the Emergent Vortices
• Chaos from Equivariant Fields on Fuzzy $S^4$
• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories
• Equivariant Fields in an $SU(\mathcal{N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
• A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions