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 ZM⩾3R 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 μ term.
Highlights
The scheme of supersymmetric grand unification provides an attractive framework for physics beyond the standard model (SM) of particle physics
This section is devoted to the proof that it is impossible to construct a grand unified theories (GUTs) in four dimensions with a finite number of multiplets that leads to the minimal supersymmetric standard model (MSSM) with a residual R symmetry
An appealing feature of the orbifold models is that there the discrete R symmetries are not imposed by hand, rather they originate from the Lorentz symmetry of compact dimensions [21], and their appearance can be related to the fact that orbifolds are highly symmetric compactifications
Summary
The scheme of supersymmetric grand unification provides an attractive framework for physics beyond the standard model (SM) of particle physics. The most compelling explanation of the smallness of neutrino masses is due to the see–saw mechanism [2], which appears to require the see–saw scale to be close to MGUT. Despite all these hints the scheme of grand unified theories (GUTs) does not yet provide us with a clear picture. We shall prove that for a spontaneously broken GUT symmetry (based on a simple Lie group) in four dimensions one cannot get the exact MSSM with residual R symmetries This allows us to conclude that a ‘natural’ solution to the doublet–triplet problem is not available in four dimensions.
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