Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking

TL;DR

This paper explores how magnetic flux on CP(1) influences dimensional reduction of Yang-Mills-Dirac theories, leading to dynamical symmetry breaking, massless chiral fermions, and a rich spectrum of particles in the effective lower-dimensional theory.

Contribution

It introduces a novel reduction scheme incorporating magnetic flux effects, resulting in exactly massless chiral fermions and detailed symmetry breaking patterns.

Findings

Magnetic flux induces dynamical symmetry breaking.

Massless chiral fermions emerge naturally in the reduced theory.

Explicit examples of particle spectra and symmetry breaking are provided.

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.