Spontaneous reduction of noncommutative gauge symmetry and model building

TL;DR

This paper introduces a mechanism for spontaneous, gauge-invariant reduction of noncommutative gauge theories, enabling the construction of a noncommutative Standard Model that naturally reproduces the usual particle spectrum and charge quantization.

Contribution

It presents a novel gauge-invariant reduction mechanism for noncommutative gauge theories and applies it to develop a consistent noncommutative Standard Model.

Findings

Mechanism for gauge-invariant reduction via gauge-invariant field condensation.

Construction of an anomaly-free noncommutative Standard Model.

Natural charge quantization for quarks and leptons.

Abstract

We propose a mechanism for the spontaneous (gauge-invariant) reduction of noncommutative ${\cal U}(n)$ gauge theories down to SU(n). This can be achieved through the condensation of composite ${\cal U}(n)$ gauge invariant fields that involves half-infinite Wilson lines in trace-U(1) noninvariant and SU(n) preserving direction. Based on this mechanism we discuss anomaly-free fully gauge invariant noncommutative Standard Model based on the minimal gauge group ${\cal U}(3)\times {\cal U}(2)\times {\cal U}(1)$, previously proposed, and show how it can be consistently reduced to the Standard Model with the usual particle spectrum. Charge quantization for quarks and leptons naturally follows from the model.