SO(10) GUT in Four and Five Dimensions: A Review

TL;DR

This review discusses SO(10) grand unified theories in four and five dimensions, emphasizing a minimal SUSY GUT model that predicts fermion masses, neutrino properties, and potential new physics, with detailed symmetry breaking analysis.

Contribution

It provides an explicit construction of the Higgs superpotential and symmetry breaking pattern, revealing multiple intermediate energy scales in minimal SUSY SO(10) GUTs.

Findings

Reproduces low energy fermion data with some lepton mixing angle discrepancies

Predicts phenomena like neutrinoless double beta decay and lepton flavor violation

Shows the GUT to SM transition involves multiple intermediate scales

Abstract

We review SO(10) grand unified theories (GUTs) in four and five dimensions (4D and 5D). The renormalizable minimal SO(10) SUSY GUT is the central theme of this review. It is very predictive and makes it possible to construct all mass matrices including those of the Dirac and heavy right-handed Majorana neutrinos. So it is not only able to reproduce all the low energy data, except for too larger $\theta_{13}$ in the lepton mixing angles (which can be evaded without spoiling the basic ingredients), but also predicts almost all new physics beyond the standard model (SM) like neutrinoless double beta decay, the electric and magnetic dipole moments of the quark-lepton, lepton flavour violation, leptogenesis etc. To be very predictive, on the other hand, implies that predictions are unambiguous and they are always exposed to severe compatibilities with observations as well as to a conceptual consistency check. The explicit construction of the Higgs superpotential and the explicit display of a symmetry breaking pattern from GUT to the SM show that the naive desert from the SM to GUT in the minimal supersymmetric standard model (MSSM) is a too simplified concept and we have many definitely determined intermediate energy scales in general. (The details should be referred to pdf.)