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arXiv · 1001.2703

Noncommutative gauge theory and symmetry breaking in matrix models

Harald Grosse·Fedele Lizzi·Harold Steinacker
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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 4 dimensions, a 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 x SU(2)_L x U(1)_Q (resp. SU(3)_c x 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.

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Harald Grosse, Fedele Lizzi, Harold Steinacker. 2010-01-15. Noncommutative gauge theory and symmetry breaking in matrix models. https://doi.org/10.1103/physrevd.81.085034

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