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2009

Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking

Dolan, Brian P., Szabo, Richard J.

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We consider SU(2)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds of the form M x CP(1), with emphasis on the effects of non-trivial magnetic flux on CP(1).

The reduction of Yang-Mills fields gives a chain of coupled Yang-Mills-Higgs systems on M with a Higgs potential leading to dynamical symmetry breaking, as a consequence of the monopole fields.
The reduction of SU(2)-symmetric fermions gives massless Dirac fermions on M transforming under the low-energy gauge group with Yukawa couplings, again as a result of the internal U(1) fluxes.
The tower of massive fermionic Kaluza-Klein states also has Yukawa interactions and admits a natural SU(2)-equivariant truncation by replacing CP(1) with a fuzzy sphere.

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