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 (21)

• Dimensional Reduction of the Heterotic String over nearly-Kaehler manifolds
• On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes
• Double quiver gauge theory and nearly Kahler flux compactifications
• Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds
• Instantons and Yang-Mills Flows on Coset Spaces
• Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices
• Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
• Dimensional Reduction and Vacuum Structure of Quiver Gauge Theory
• Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons
• Covariant Quiver Gauge Theories
• Yang-Mills Equations of Motion for the Higgs Sector of SU(3)-Equivariant Quiver Gauge Theories
• Geometry and Energy of Non-abelian Vortices
• Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions
• Equivariant Dimensional Reduction and Quiver Gauge Theories
• Dimensional reduction over the quantum sphere and non-abelian q-vortices
• Equivariant Reduction of U(4) Gauge Theory over S_F^2 x S_F^2 and the Emergent Vortices
• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories
• Equivariant Fields in an $SU(\mathcal{N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
• Solitons and Yukawa Couplings in Nearly Kahler Flux Compactifications
• A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions
• Nearly-Kaehler dimensional reduction of the heterotic string