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Title: General Solution to the U(1) Anomaly Equations

Abstract

The anomaly cancellation equations for the $U(1)$ gauge group can be written as a cubic equation in $n-1$ integer variables, where $n$ is the number of Weyl fermions carrying the $U(1)$ charge. We solve this Diophantine cubic equation by providing a parametrization of the charges in terms of $n-2$ integers, and prove that this is the most general solution.

Authors:
ORCiD logo [1];  [2]; ORCiD logo [2]
  1. Univ. de São Paulo, São Paulo (Brasil)
  2. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1571315
Alternate Identifier(s):
OSTI ID: 1568881
Report Number(s):
arXiv:1905.13729; FERMILAB-PUB-19-252-T
Journal ID: ISSN 0031-9007; PRLTAO; oai:inspirehep.net:1737609
Grant/Contract Number:  
AC02-07CH11359
Resource Type:
Published Article
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 123; Journal Issue: 15; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Costa, Davi B., Dobrescu, Bogdan A., and Fox, Patrick J. General Solution to the U(1) Anomaly Equations. United States: N. p., 2019. Web. doi:10.1103/PhysRevLett.123.151601.
Costa, Davi B., Dobrescu, Bogdan A., & Fox, Patrick J. General Solution to the U(1) Anomaly Equations. United States. doi:10.1103/PhysRevLett.123.151601.
Costa, Davi B., Dobrescu, Bogdan A., and Fox, Patrick J. Wed . "General Solution to the U(1) Anomaly Equations". United States. doi:10.1103/PhysRevLett.123.151601.
@article{osti_1571315,
title = {General Solution to the U(1) Anomaly Equations},
author = {Costa, Davi B. and Dobrescu, Bogdan A. and Fox, Patrick J.},
abstractNote = {The anomaly cancellation equations for the $U(1)$ gauge group can be written as a cubic equation in $n-1$ integer variables, where $n$ is the number of Weyl fermions carrying the $U(1)$ charge. We solve this Diophantine cubic equation by providing a parametrization of the charges in terms of $n-2$ integers, and prove that this is the most general solution.},
doi = {10.1103/PhysRevLett.123.151601},
journal = {Physical Review Letters},
number = 15,
volume = 123,
place = {United States},
year = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevLett.123.151601

Citation Metrics:
Cited by: 1 work
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