Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking

Abstract

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. In this approach it is possible to obtain exactly massless chiral fermions in the effective field theory with Yukawa interactions, without any further requirements. We work out the spontaneous symmetry breaking patterns and determine the complete physical particle spectrum in a number of explicit examples.

23 pages; v2: minor corrections, references added - final version to appear in JHEP

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Cited by in corpus (3)

• Dimensional Reduction of the Heterotic String over nearly-Kaehler manifolds
• Instantons and Yang-Mills Flows on Coset Spaces
• Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices