Noncommutative gauge theory and symmetry breaking in matrix models

TL;DR

This paper demonstrates how standard model particles and gauge symmetry breaking can be realized within a noncommutative gauge theory framework derived from matrix models, connecting to emergent gravity and string theory concepts.

Contribution

It introduces a novel approach to embed the standard model in noncommutative gauge theories from matrix models, including spontaneous symmetry breaking and emergent gravity mechanisms.

Findings

Standard model fields realized in noncommutative gauge theory

Spontaneous symmetry breaking to standard model gauge group

Emergent gravity from trace-U(1) sector

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.