Dolan, Brian P. and Szabo, Richard J.
Dimensional Reduction and
Vacuum Structure of Quiver Gauge Theory.
Journal of High Energy Physics, 2009 (8-038).
We describe the structure of the vacuum states of quiver gauge theories obtained via dimensional
reduction over homogeneous spaces, in the explicit example of SU(3)-equivariant dimensional
reduction of Yang-Mills-Dirac theory on manifolds of the form M × CP2. We pay particular
attention to the role of topology of background gauge fields on the internal coset spaces, in
this case U(1) magnetic monopoles and SU(2) instantons on CP2. The reduction of Yang-Mills
theory induces a quiver gauge theory involving coupled Yang-Mills-Higgs systems on M with
a Higgs potential leading to dynamical symmetry breaking. The criterion for a ground state
of the Higgs potential can be written as the vanishing of a non-abelian Yang-Mills flux on the
quiver diagram, regarded as a lattice with group elements attached to the links. The reduction of
SU(3)-symmetric fermions yields Dirac fermions on M transforming under the low-energy gauge
group with Yukawa couplings. The fermionic zero modes on CP2 yield exactly massless chiral
fermions on M, though there is a unique choice of spinc structure on CP2 for which some of
the zero modes can acquire masses through Yukawa interactions. We work out the spontaneous
symmetry breaking patterns and determine the complete physical particle spectrum in a number
of explicit examples, some of which possess quantum number assignments qualitatively analogous
to the manner in which vector bosons, quarks and leptons acquire masses in the standard model.
||Preprint version of published article. The original publication is available at www.springerlink.com. B.P.D. wishes to thank the Dublin Institute of Advanced Studies for financial support, and also the
Perimeter Institute for Theoretical Physics, where this work was completed, for their hospitality
and support. The work of R.J.S. was supported in part by the EU-RTN Network Grant MRTNCT-
||Dimensional Reduction; Vacuum Structure; Quiver Gauge Theory; Yang-Mills-Dirac theory;
||Faculty of Science and Engineering > Mathematical Physics
Dr. Brian Dolan
||26 Aug 2011 15:32
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||Journal of High Energy Physics
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