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:
- 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
Other availability
Cited by: 14 works
Citation information provided by
Web of Science
Web of Science
Figures / Tables:

All figures and tables
(1 total)
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Minimal anomaly-free chiral fermion sets and gauge coupling unification
journal, December 2014
- Cebola, Luís M.; Emmanuel-Costa, D.; Felipe, R. González
- Physical Review D, Vol. 90, Issue 12
An anomaly-free atlas: charting the space of flavour-dependent gauged U(1) extensions of the Standard Model
journal, February 2019
- Allanach, B. C.; Davighi, Joe; Melville, Scott
- Journal of High Energy Physics, Vol. 2019, Issue 2
Number-theory dark matter
journal, May 2011
- Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T.
- Physics Letters B, Vol. 699, Issue 5
Imperfect mirror copies of the standard model
journal, August 2016
- Berryman, Jeffrey M.; de Gouvêa, André; Hernández, Daniel
- Physical Review D, Vol. 94, Issue 3
Axial vector Z ′ and anomaly cancellation
journal, May 2017
- Ismail, Ahmed; Keung, Wai-Yee; Tsao, Kuo-Hsing
- Nuclear Physics B, Vol. 918
Effect of Anomalies on Quasi-Renormalizable Theories
journal, July 1972
- Gross, David J.; Jackiw, R.
- Physical Review D, Vol. 6, Issue 2
Simple model for (3+2) neutrino oscillations
journal, July 2004
- Babu, K. S.; Seidl, Gerhart
- Physics Letters B, Vol. 591, Issue 1-2
Anomalous Ward Identities in Spinor Field Theories
journal, August 1969
- Bardeen, William A.
- Physical Review, Vol. 184, Issue 5
Dark discrete gauge symmetries
journal, February 2011
- Batell, Brian
- Physical Review D, Vol. 83, Issue 3
Fermion mass hierarchy and proton stability from nonanomalous in supersymmetric
journal, July 2008
- Chen, Mu-Chun; Jones, D. R. Timothy; Rajaraman, Arvind
- Physical Review D, Vol. 78, Issue 1
Gauge Theories Without Anomalies
journal, July 1972
- Georgi, Howard; Glashow, Sheldon L.
- Physical Review D, Vol. 6, Issue 2
Surprises from complete vector portal theories: New insights into the dark sector and its interplay with Higgs physics
journal, November 2017
- Cui, Yanou; D’Eramo, Francesco
- Physical Review D, Vol. 96, Issue 9
Anomaly-free sets of fermions
journal, August 2006
- Batra, Puneet; Dobrescu, Bogdan A.; Spivak, David
- Journal of Mathematical Physics, Vol. 47, Issue 8
Axial-Vector Vertex in Spinor Electrodynamics
journal, January 1969
- Adler, Stephen L.
- Physical Review, Vol. 177, Issue 5
New chiral fermions, a new gauge interaction, Dirac neutrinos, and dark matter
journal, October 2015
- de Gouvêa, André; Hernández, Daniel
- Journal of High Energy Physics, Vol. 2015, Issue 10
Gravitation, gauge theories and differential geometry
journal, December 1980
- Eguchi, Tohru; Gilkey, Peter B.; Hanson, Andrew J.
- Physics Reports, Vol. 66, Issue 6
Models of neutrino mass with a low cutoff scale
journal, June 2005
- Davoudiasl, Hooman; Kitano, Ryuichiro; Kribs, Graham D.
- Physical Review D, Vol. 71, Issue 11
An anomaly-free version of Weinberg's model
journal, April 1972
- Bouchiat, C.; Iliopoulos, J.; Meyer, Ph.
- Physics Letters B, Vol. 38, Issue 7
Works referencing / citing this record:
Hypercharge quantisation and Fermat's last theorem
journal, January 2020
- Lohitsiri, Nakarin; Tong, David
- SciPost Physics, Vol. 8, Issue 1
Anomaly free Froggatt-Nielsen models of flavor
journal, October 2019
- Smolkovič, Aleks; Tammaro, Michele; Zupan, Jure
- Journal of High Energy Physics, Vol. 2019, Issue 10
Notes on anomalies, elliptic curves and the BS-D conjecture
journal, December 2019
- Lü, Yongchao; Minahan, Joseph A.
- Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 2
Classification of anomaly-free 2HDMs with a gauged symmetry
journal, December 2019
- Nottensteiner, Franz; Ordell, Astrid; Pasechnik, Roman
- Physical Review D, Vol. 100, Issue 11
Gauging the accidental symmetries of the standard model, and implications for the flavor anomalies
journal, January 2020
- Altmannshofer, Wolfgang; Davighi, Joe; Nardecchia, Marco
- Physical Review D, Vol. 101, Issue 1
Chiral Froggatt-Nielsen models, gauge anomalies and flavourful axions
text, January 2020
- Bonnefoy, Quentin Rene Christian; Dudas, E.; Pokorski, S.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.