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.
- Publication Date:
- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- 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; 151601
- Grant/Contract Number:
- AC02-07CH11359
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 123 Journal Issue: 15; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society
- 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}
}
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevLett.123.151601
DOI: 10.1103/PhysRevLett.123.151601
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Cited by: 14 works
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Figures / Tables:
TABLE I: Primitive solutions to the anomaly equations for 6 fermions in canonical form for $z$1 ≤ 12. A choice of the $k$1, $k$2, ℓ1, ℓ 2 parameters and the greatest common divisor that generate the primitive solution from the set (17) are shown.
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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.