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.

5 pages

References in corpus (12)

• Dark Discrete Gauge Symmetries
• An Anomaly-free Atlas: charting the space of flavour-dependent gauged $U(1)$ extensions of the Standard Model
• Axial Vector $Z^{\prime }$ and Anomaly Cancellation
• Anomaly-Free Sets of Fermions
• Anomaly-free Model Building with Algebraic Geometry
• Surprises from Complete Vector Portal Theories: New Insights into the Dark Sector and its Interplay with Higgs Physics
• Models of Neutrino Mass with a Low Cutoff Scale
• Simple Model for (3+2) Neutrino Oscillations
• Number-Theory Dark Matter
• Fermion Mass Hierarchy and Proton Stability from Non-anomalous U(1)_F in SUSY SU(5)
• Imperfect Mirrors of the Standard Model
• Minimal anomaly-free chiral fermion sets and gauge coupling unification

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