Spontaneous reduction of noncommutative gauge symmetry and model building

Abstract

We propose a mechanism for the spontaneous (gauge-invariant) reduction of noncommutative $\mathcal{U}(n)$ gauge theories down to SU(n). This can be achieved through the condensation of composite $\mathcal{U}(n)$ 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 $\mathcal{U}(3)\times \mathcal{U}(2)\times \mathcal{U}(1)$, 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.

7 pages, no figures

References in corpus (2)

• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Noncommutative Standard Modelling

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