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Geometric general solution to the U(1) anomaly equations

Published version
Peer-reviewed

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Authors

Gripaios, Ben 
Tooby-Smith, Joseph  ORCID logo  https://orcid.org/0000-0003-2831-598X

Abstract

Abstract: Costa et al. [Phys. Rev. Lett.123 (2019) 151601] recently gave a general solution to the anomaly equations for n charges in a U(1) gauge theory. ‘Primitive’ solutions of chiral fermion charges were parameterised and it was shown how operations performed upon them (concatenation with other primitive solutions and with vector-like solutions) yield the general solution. We show that the ingenious methods used there have a simple geometric interpretation, corresponding to elementary constructions in number theory. Viewing them in this context allows the fully general solution to be written down directly, without the need for further operations. Our geometric method also allows us to show that the only operation Costa et al. require is permutation. It also gives a variety of other, qualitatively similar, parameterisations of the general solution, as well as a qualitatively different (and arguably simpler) form of the general solution for n even.

Description

Keywords

Regular Article - Theoretical Physics, Anomalies in Field and String Theories, Gauge Symmetry

Journal Title

Journal of High Energy Physics

Conference Name

Journal ISSN

1029-8479

Volume Title

2020

Publisher

Springer Berlin Heidelberg