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 μ. 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 μ and dimension-5 proton decay problems are solved simultaneously by an order four discrete R symmetry. We also comment on the higher-dimensional origin of this symmetry.
Highlights
Introduction and OutlineThe minimal supersymmetric Standard Model (MSSM) provides an attractive scheme for physics beyond the Standard Model (SM) of particle physics
We 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
Given that P6 is incompatible with grand unification, we see that this symmetry cannot be used to solve the most severe problems of GUT models
Summary
The minimal supersymmetric Standard Model (MSSM) provides an attractive scheme for physics beyond the Standard Model (SM) of particle physics. In the context of unified theories, the perhaps most important property of the MSSM is that it provides us with the very compelling picture of precision gauge coupling unification.[1] That is, if one assumes that the superpartners have masses of the order TeV and extrapolates the gauge couplings gi of the SM gauge factors SU(3), SU(2) and U(1) to higher energies, one finds that they meet with a high precision at the scale of a few × 1016 GeV. The conventional solutions to the MSSM problems are, arguably, not fully satisfactory
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