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General solution to the U(1) anomaly equations
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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.
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Cited by 1 Pith paper
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Anomaly cancellation for two $U(1)$ factors
Abelian anomaly cancellation for rank-K U(1) summands equates to finding (K-1)-planes on a cubic hypersurface over Q; for K=2 and six fermions this is the Fano surface of the Segre cubic, whose rational components ful...
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