Dimensional Reduction and Vacuum Structure of Quiver Gauge Theory

Dolan, Brian P. and Szabo, Richard J. (2009) Dimensional Reduction and Vacuum Structure of Quiver Gauge Theory. Journal of High Energy Physics, 2009 (8-038). pp. 1-37. ISSN 1126-6708

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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.

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 EU-RTN Network Grant MRTNCT- 2004-005104 .
Keywords: Dimensional Reduction; Vacuum Structure; Quiver Gauge Theory; Yang-Mills-Dirac theory;
Academic Unit: Faculty of Science and Engineering > Mathematical Physics
Item ID: 2676
Identification Number: doi: 10.1088/1126-6708/2009/08/038
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

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