## SciPost Submission Page

# Hypercharge Quantisation and Fermat's Last Theorem

### by Nakarin Lohitsiri, David Tong

#### - Published as SciPost Phys. 8, 009 (2020)

### 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

See full Ontology or Topics database.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.