## 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
- Submissions/Reports

### 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.

### Cited by 5

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{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