Noncommutative gauge theory and symmetry breaking in matrix models

We show how the fields and particles of the standard model can be naturally realized in non-commutative 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) 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.