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Anomaly cancellation with an extra gauge boson
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Many extensions of the Standard Model include an extra gauge boson, whose couplings to fermions are constrained by the requirement that anomalies cancel. We find a general solution to the resulting diophantine equations in the plausible case where the chiral fermion content is that of the Standard Model plus 3 right-handed neutrinos.
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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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