Supersymmetric unification and R symmetries

TL;DR

This paper reviews the importance of R symmetries in supersymmetric unification, highlighting their role in forbidding the mu term, their absence in 4D GUTs, and their potential in higher-dimensional models and string theory.

Contribution

It demonstrates that R symmetries are essential for natural solutions to the mu problem and discusses their realization in higher-dimensional GUTs and string-derived models.

Findings

R symmetries can forbid the mu term in supersymmetric models.

Conventional 4D GUTs lack R symmetries, complicating the doublet-triplet splitting.

Higher-dimensional GUTs and string models can incorporate R symmetries to solve key problems.

Abstract

We review the role of R symmetries in models of supersymmetric unification in four and more dimensions, and in string theory. We show that, if one demands anomaly freedom and fermion masses, only R symmetries can forbid the supersymmetric Higgs mass term mu. We then review the proof that R symmetries are not available in conventional grand unified theories (GUTs) and argue that this prevents natural solutions to the doublet-triplet splitting problem in four dimensions. On the other hand, higher-dimensional GUTs do not suffer from this problem. We briefly comment on an explicit string-derived model in which the mu and dimension five proton decay problems are solved simultaneously by an order four discrete R symmetry. We also comment on the higher-dimensional origin of this symmetry.