Hypercharge quantisation and Fermat's last theorem

Lohitsiri, Nakarin; Tong, David

doi:10.21468/SciPostPhys.8.1.009

SciPost Physics

Hypercharge quantisation and Fermat's last theorem

Nakarin Lohitsiri, David Tong

SciPost Phys. 8, 009 (2020) · published 23 January 2020

doi: 10.21468/SciPostPhys.8.1.009
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.8.1.009
TI  - Hypercharge quantisation and Fermat's last theorem
PY  - 2020/01/23
UR  - https://scipost.org/SciPostPhys.8.1.009
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 8
IS  - 1
SP  - 009
A1  - Lohitsiri, Nakarin
AU  - Tong, David
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.8.1.009,
	title={{Hypercharge quantisation and Fermat's last theorem}},
	author={Nakarin Lohitsiri and David Tong},
	journal={SciPost Phys.},
	volume={8},
	pages={009},
	year={2020},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.8.1.009},
	url={https://scipost.org/10.21468/SciPostPhys.8.1.009},
}

Cited by 5

Ontology / Topics

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Gauge theory Quantum field theory (QFT) Standard Model

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Nakarin Lohitsiri,
¹ ² David Tong

Funders for the research work leading to this publication

Ministry of Science and Technology of Thailand (through Organization: กระทรวงวิทยาศาสตร์และเทคโนโลยี / Ministry of Science and Technology Thailand [MOST])
Science and Technology Facilities Council [STFC]
Simons Foundation
Trinity College, University of Cambridge