No-go theorems for R symmetries in four-dimensional GUTs

TL;DR

This paper proves that four-dimensional GUT models with simple gauge groups cannot exactly reproduce the MSSM with unbroken R symmetries, highlighting fundamental limitations in 4D GUT constructions.

Contribution

It establishes a no-go theorem showing the impossibility of certain 4D GUT models with R symmetries that yield the MSSM or its extensions.

Findings

No 4D GUT with simple gauge group can produce the exact MSSM with unbroken R symmetry.

GUT models with extra dimensions are not constrained by this no-go theorem.

Impossible to construct a 4D GUT leading to MSSM plus an anomaly-free symmetry forbidding the mu term.

Abstract

We prove that it is impossible to construct a grand unified model, based on a simple gauge group, in four dimensions that leads to the exact MSSM, nor to a singlet extension, and possesses an unbroken R symmetry. This implies that no MSSM model with either a Z_{M>=3}^R or U(1)_R symmetry can be completed by a four-dimensional GUT in the ultraviolet. However, our no-go theorem does not apply to GUT models with extra dimensions. We also show that it is impossible to construct a 4D GUT that leads to the MSSM plus an additional anomaly-free symmetry that forbids the mu term.