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

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10.1016.j.nuclphysb.2009.06.031.pdf

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2009-11-01

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Harland, Derek
Kürkcüoğlu, Seçkin

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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 comutative 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.

Subject Keywords

Nuclear and High Energy Physics

URI

https://hdl.handle.net/11511/38464

Journal

NUCLEAR PHYSICS B

DOI

https://doi.org/10.1016/j.nuclphysb.2009.06.031

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Department of Physics, Article

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Citation Formats

D. Harland and S. Kürkcüoğlu, “Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices,” NUCLEAR PHYSICS B, pp. 380–398, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38464.