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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.

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Published as SciPost Phys. 8, 009 (2020)

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