Non-Abelian discrete R symmetries

TL;DR

This paper explores non-Abelian discrete R symmetries in supersymmetric models, deriving anomaly constraints, and demonstrating their potential to address key issues like mu-term and proton decay within unified flavor symmetry frameworks.

Contribution

It introduces anomaly constraints for non-Abelian discrete R symmetries and presents an example model combining these with flavor symmetries to solve MSSM problems.

Findings

Novel Green-Schwarz anomaly cancellation patterns

Perfect groups are always anomaly-free

Example model unifies R symmetries with flavor 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.