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Hypercharge Quantisation and Fermat's Last Theorem

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arxiv 1907.00514 v3 pith:3HOOYBQQ submitted 2019-07-01 hep-th hep-ph

Nakarin Lohitsiri , David Tong This is my paper · ORCID
classification hep-thhep-ph
keywords hyperchargeanomaliesgaugequantisedanomalyargumentassignmentsautomatically
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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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  1. Notes on anomalies, elliptic curves and the BS-D conjecture

    hep-th 2019-08 accept novelty 6.0 of 10

    For a compact U(1) extension with SU(2) triplets, anomaly cancellation gives one nontrivial hypercharge assignment for N=3, two for N=9, and infinitely many for all other N.

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