Noncommutative gauge theory and symmetry breaking in matrix models

Harald Grosse, Fedele Lizzi, and Harold Steinacker
Phys. Rev. D 81, 085034 – Published 23 April 2010

Abstract

We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an SU(n) gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to SU(3)c×SU(2)L×U(1)Q [resp. SU(3)c×U(1)Q], which couples appropriately to all fields in the standard model. An additional U(1)B gauge group arises which is anomalous at low energies, while the trace-U(1) sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.

  • Received 25 January 2010

DOI:https://doi.org/10.1103/PhysRevD.81.085034

©2010 American Physical Society

Authors & Affiliations

Harald Grosse1,*, Fedele Lizzi2,3,†, and Harold Steinacker1,‡

  • 1Department of Physics, University of Vienna, Boltzmanngasse5, A-1090 Vienna, Austria
  • 2Dipartimento di Scienze Fisiche, Università di Napoli Federico II and INFN, Sezione di Napoli, Via Cintia, 80126 Napoli, Italy
  • 3High Energy Physics Group, Departament d’Estructura i Constituents de la Matèria and Institut de Ciències del Cosmos Universitat de Barcelona Barcelona, Catalonia, Spain

  • *harald.grosse@univie.ac.at
  • fedele.lizzi@na.infn.it
  • harold.steinacker@univie.ac.at

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Issue

Vol. 81, Iss. 8 — 15 April 2010

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