Anomaly-free model building with algebraic geometry

Johan Rathsman, Felix Tellander

Research output: Contribution to journalArticlepeer-review


We present a method to find anomaly-free gauged Froggatt-Nielsen type models using results from algebraic geometry. These methods should be of general interest for model building beyond the Standard Model (SM) when rational charges are required. We consider models with a gauged U(1) flavor symmetry with one flavon and two Higgs doublets and three right-handed SM singlets to provide three model examples based on different physical assumptions. The models we study are anomaly-free with no SM neutral heavy chiral fermions, anomaly-free with SM neutral heavy chiral fermions, and supersymmetric with SM neutral heavy chiral fermions where the anomalies cancel via the Green-Schwarz mechanism. With these different models we show how algebraic methods may be used in model building, both to reduce the charge constraints by calculation of Gröbner bases and to find rational solutions to cubic equations using Mordell-Weil generators. Using these tools we find three phenomenologically viable models explaining the observed flavor structure.

Original languageEnglish
Article number055032
JournalPhysical Review D
Issue number5
Publication statusPublished - 2019 Sept 23

Subject classification (UKÄ)

  • Subatomic Physics


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