Hypercharge Quantisation and Fermat's Last Theorem
High Energy Physics - Theory
2020-01-29 v3 High Energy Physics - Phenomenology
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.
Cite
@article{arxiv.1907.00514,
title = {Hypercharge Quantisation and Fermat's Last Theorem},
author = {Nakarin Lohitsiri and David Tong},
journal= {arXiv preprint arXiv:1907.00514},
year = {2020}
}
Comments
2.25 pages. v2: References added. v3: More references, and comment on the right handed neutrino