Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices

Abstract

We consider a U(2) Yang-Mills theory on M x S_F^2 where M is a Riemannian manifold and S_F^2 is the fuzzy sphere. Using essentially the representation theory of SU(2) we determine the most general SU(2)-equivariant gauge field on M x S_F^2. This allows us to reduce the Yang-Mills theory on M x S_F^2 down to an abelian Higgs-type model over M. Depending on the enforcement (or non-enforcement) of a "constraint" term, the latter may (or may not) lead to the standard critically-coupled abelian Higgs model in the commutative limit, S_F^2 -> S^2. For M = R^2, we find that the abelian Higgs-type model admits vortex solutions corresponding to instantons in the original Yang-Mills theory. Vortices are in general no longer BPS, but may attract or repel according to the values of parameters.

arXiv comment20 pages, 2 figures

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• Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
• Lorentzian Fuzzy Spheres
• Dimensional Reduction and Vacuum Structure of Quiver Gauge Theory
• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
• Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions
• Dimensional reduction over the quantum sphere and non-abelian q-vortices
• Equivariant Reduction of U(4) Gauge Theory over S_F^2 x S_F^2 and the Emergent Vortices
• Intersecting branes, Higgs sector, and chirality from $\mathcal{N}=4$ SYM with soft SUSY breaking
• 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
• Non-commutativity in Unified Theories and Gravity
• A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions
• Equivariance on Discrete Space and Yang-Mills-Higgs Model