Dolan, Brian P. and Szabo, Richard J.
(2009)
Dimensional Reduction and
Vacuum Structure of Quiver Gauge Theory.
Journal of High Energy Physics, 2009 (8038).
pp. 137.
ISSN 11266708
Abstract
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 YangMillsDirac 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 YangMills
theory induces a quiver gauge theory involving coupled YangMillsHiggs 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 nonabelian YangMills 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 lowenergy 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.
Item Type: 
Article

Additional Information: 
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 EURTN Network Grant MRTNCT
2004005104 . 
Keywords: 
Dimensional Reduction; Vacuum Structure; Quiver Gauge Theory; YangMillsDirac theory; 
Subjects: 
Science & Engineering > Mathematical Physics 
Item ID: 
2676 
Identification Number: 
doi: 10.1088/11266708/2009/08/038 
Depositing User: 
Dr. Brian Dolan

Date Deposited: 
26 Aug 2011 15:32 
Journal or Publication Title: 
Journal of High Energy Physics 
Publisher: 
Institute of Physics 
Refereed: 
Yes 
URI: 

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