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arXiv · 1907.00514

Hypercharge Quantisation and Fermat's Last Theorem

Nakarin Lohitsiri·David Tong
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Abstract

What values of the Standard Model hypercharges result in a mathematically consistent quantum field theory? We show that the constraints imposed by the lack of gauge anomalies can be recast as the equation x^3 + y^3 = z^3. If hypercharge is quantised, then x, y and z must be integers. The trivial (and only) solutions, with x=0 or y=0, reproduce the hypercharge assignments seen in Nature. This argument does not rely on the mixed gauge-gravitational anomaly, which is automatically vanishing if hypercharge is quantised and the gauge anomalies vanish.

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Nakarin Lohitsiri, David Tong. 2019-07-01. Hypercharge Quantisation and Fermat's Last Theorem. https://doi.org/10.21468/scipostphys.8.1.009

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