SciPost Submission Page
Hypercharge Quantisation and Fermat's Last Theorem
by Nakarin Lohitsiri, David Tong
- Published as SciPost Phys. 8, 009 (2020)
|As Contributors:||David Tong|
|Arxiv Link:||https://arxiv.org/abs/1907.00514v3 (pdf)|
|Submitted by:||Tong, David|
|Submitted to:||SciPost Physics|
|Subject area:||Quantum Physics|
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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Published as SciPost Phys. 8, 009 (2020)
Author comments upon resubmission
List of changes
Added several new references as requested in the first report.
Added an extra, final paragraph discussing the right-handed neutrino, as requested in the second report.