Geometric general solution to the U(1) anomaly equations
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...
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Online Access: | http://link.springer.com/article/10.1007/JHEP05(2020)065 |
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doaj-6dfb6e5763d449f29bf4a982b0edbec22020-11-25T02:05:55ZengSpringerOpenJournal of High Energy Physics1029-84792020-05-012020511110.1007/JHEP05(2020)065Geometric general solution to the U(1) anomaly equationsB C. Allanach0Ben Gripaios1Joseph Tooby-Smith2DAMTP, University of CambridgeCavendish Laboratory, University of CambridgeCavendish Laboratory, University of CambridgeAbstract 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.http://link.springer.com/article/10.1007/JHEP05(2020)065Anomalies in Field and String TheoriesGauge Symmetry |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
B C. Allanach Ben Gripaios Joseph Tooby-Smith |
spellingShingle |
B C. Allanach Ben Gripaios Joseph Tooby-Smith Geometric general solution to the U(1) anomaly equations Journal of High Energy Physics Anomalies in Field and String Theories Gauge Symmetry |
author_facet |
B C. Allanach Ben Gripaios Joseph Tooby-Smith |
author_sort |
B C. Allanach |
title |
Geometric general solution to the U(1) anomaly equations |
title_short |
Geometric general solution to the U(1) anomaly equations |
title_full |
Geometric general solution to the U(1) anomaly equations |
title_fullStr |
Geometric general solution to the U(1) anomaly equations |
title_full_unstemmed |
Geometric general solution to the U(1) anomaly equations |
title_sort |
geometric general solution to the u(1) anomaly equations |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2020-05-01 |
description |
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. |
topic |
Anomalies in Field and String Theories Gauge Symmetry |
url |
http://link.springer.com/article/10.1007/JHEP05(2020)065 |
work_keys_str_mv |
AT bcallanach geometricgeneralsolutiontotheu1anomalyequations AT bengripaios geometricgeneralsolutiontotheu1anomalyequations AT josephtoobysmith geometricgeneralsolutiontotheu1anomalyequations |
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1724936163710468096 |