Anomaly of discrete family symmetries and gauge coupling unification

Details Anomaly of discrete family symmetries and gauge coupling unification Anomaly of discrete family symmetries and gauge coupling unification

2006-10-24

arxiv.org/abs/hep-ph/0610305v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

Talk given at the Summer Institute 2006 (SI2006), APCTP, Pohang, Korea. 23-30 Aug 2006

Scientific paper

10.1142/S0218301307006812

Anomaly of discrete symmetries can be defined as the Jacobian of the path-integral measure. We assume that an anomalous discrete symmetry at low energy is remnant of an anomaly free discrete symmetry, and that its anomaly is cancelled by the Green-Schwarz(GS) mechanism at a more fundamental scale. If the Kac-Moody levels k_i assume non-trivial values, the GS cancellation conditions of anomaly modify the ordinary unification of gauge couplings. This is most welcome, because for a renormalizable model to be realistic any non-abelian family symmetry, which should not be hardly broken low-energy, requires multi SU(2)_L doublet Higgs fields. As an example we consider a recently proposed supersymmetric model with Q_6 family symmetry. In this example, k_2=1, k_3=3 satisfies the GS conditions and the gauge coupling unification appears close to the Planck scale.

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