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General solution to the U(1) anomaly equations · Around

2019

General solution to the U(1) anomaly equations

Costa, Davi B., Dobrescu, Bogdan A., Fox, Patrick J.

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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.

Built on

J. Rathsman and F. Tellander, “Anomaly-free model building with algebraic geometry,” arXiv:1902.08529
Original
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For a review, see T. Eguchi, P. B. Gilkey and A. J. Hanson, “Gravitation, gauge theories and differential geometry,” Phys. Rept. 66
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Earlier work this paper cites.

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A. de Gouvea and D. Hernandez, “New chiral fermions, a new gauge interaction, Dirac neutrinos, and dark matter,” JHEP 1510
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Then

K. Nakayama, F. Takahashi, T. T. Yanagida, “Number-Theory Dark Matter,” Phys. Lett. B 699
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B. C. Allanach, J. Davighi, S. Melville, “An anomaly-free Atlas: charting the space of flavour-dependent gauged U ⁡ ( 1 ) U(1) extensions of the Standard Model,” JHEP 1902
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