Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices
| Autor: | Harland, Derek, Kurkcuoglu, Seckin |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Nucl.Phys.B821:380-398,2009 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2009.06.031 |
| Popis: | 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. Comment: 20 pages, 2 figures |
| Databáze: | arXiv |
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