Non-Abelian discrete R symmetries

Abstract

We discuss non-Abelian discrete R symmetries which might have some conceivable relevance for model building. The focus is on settings with N=1 supersymmetry, where the superspace coordinate transforms in a one-dimensional representation of the non-Abelian discrete symmetry group. We derive anomaly constraints for such symmetries and find that novel patterns of Green-Schwarz anomaly cancellation emerge. In addition we show that perfect groups, also in the non-R case, are always anomaly-free. An important property of models with non-Abelian discrete R symmetries is that superpartners come in different representations of the group. We present an example model, based on a semidirect product of a Z_3 and a Z_8^R symmetry, to discuss generic features of models which unify discrete R symmetries, entailing solutions to the mu and proton decay problems of the MSSM, with non-Abelian discrete flavor symmetries.

21 pages

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• The first string-derived eclectic flavor model with realistic phenomenology
• Top-Down Anatomy of Flavor Symmetry Breakdown
• Linking Natural Supersymmetry to Flavour Physics
• Delta(54) flavor phenomenology and strings
• A low-scale flavon model with a $Z_N$ symmetry
• Anomalous Discrete Flavor Symmetry and Domain Wall Problem
• CP and other Symmetries of Symmetries
• A counterexample to the Nelson-Seiberg theorem
• Gauge anomalies of finite groups
• Note on gauge and gravitational anomalies of discrete $Z_N$ symmetries
• Completing the eclectic flavor scheme of the ${\mathbb{Z}}_2$ orbifold
• Novel Flavon Stabilization with Trimaximal Neutrino Mixing
• Anomaly-safe discrete groups