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 involve half-infinite Wilson lines in the trace-U(1) noninvariant and SU(n) preserving direction. Based on this mechanism, we discuss an 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.
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Chaichian, M., Kobakhidze, A. & Tureanu, A. Spontaneous reduction of noncommutative gauge symmetry and model building. Eur. Phys. J. C 47, 241–245 (2006). https://doi.org/10.1140/epjc/s2006-02547-1
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DOI: https://doi.org/10.1140/epjc/s2006-02547-1