Anomalies of Discrete Symmetries and Gauge Coupling Unification

T. Araki
2007 Progress of theoretical physics  
The anomaly of a discrete symmetry is defined as the Jacobian of the path-integral measure. Assuming that the anomaly at low energies is cancelled by the Green-Schwarz (GS) mechanism at a fundamental scale, we investigate possible Kac-Moody levels for anomalous discrete family symmetries. As the first example, we consider discrete abelian baryon number and lepton number symmetries in the minimal supersymmetric standard model with the see-saw mechanism, and we find that the ordinary unification
more » ... f gauge couplings is inconsistent with the GS conditions, indicating the possible existence of further Higgs doublets. We consider various recently proposed supersymmetric models with a non-abelian discrete family symmetry. In a supersymmetric example with Q_6 family symmetry, the GS conditions are such that the gauge coupling unification appears close to the Planck scale.
doi:10.1143/ptp.117.1119 fatcat:7khepf6ghraixisw7qgmt3sbea