Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2006-12-22
Prog.Theor.Phys.117:1119-1138,2007
Physics
High Energy Physics
High Energy Physics - Phenomenology
22 pages, 4 figures, many typos corrected, references added, published version
Scientific paper
10.1143/PTP.117.1119
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 of 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.
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