Heriot-Watt Mathematics Report Series
HWM09-1, 13 Jan 2009
Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking
B P Dolan and R J Szabo
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.
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