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Hypercharge Quantisation and Fermat's Last Theorem

by Nakarin Lohitsiri, David Tong

Submission summary

As Contributors: David Tong
Arxiv Link: https://arxiv.org/abs/1907.00514v3
Date accepted: 2020-01-22
Date submitted: 2020-01-16
Submitted by: Tong, David
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Quantum Physics
Approach: Theoretical

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.

Ontology / Topics

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Gauge theory Quantum field theory (QFT) Standard Model

Published as SciPost Phys. 8, 009 (2020)



Author comments upon resubmission

We thank the referees for their comments. And we apologise for the long delay in getting this updated.

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.

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