So(10) Gut in Four and Five Dimensions: A Review

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 θ 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. This situation destroys the naive gauge coupling unification in the MSSM scheme. Also the precise measurements of neutrino oscillation data have revealed several small but manifest mismatches with our predictions. Also there are arguments that it is impossible to construct a GUT theory in 4D with a finite number of multiplets that leads to the MSSM with a residual R symmetry. Of course, there are several loopholes which solve these problems in 4D. However, if we try to solve all these pathologies comprehensively, it is very attractive for us to go into extra dimensions. Extra dimension may be either warped or flat. The fifth dimension, for simplicity, is compactified on the S 1 /(Z 2 ) (warped) or on the S 1 /(Z 2 × Z ′ 2 ) (flat) orbifold with two inequivalent branes at the orbifold fixed points. In the former warped case, intermediate energy scales are translated with the positions of Higgs fields in the bulk and the fundamental scheme of the MSSM is recovered. On the other hand, in the latter flat scenario, all matter and Higgs multiplets reside on the Pati-Salam (PS) brane where the PS symmetry is manifest. There the original renormalizablity in Yukawa coupling is broken but its essential structures of mass matrices in minimal SO(10) GUT in 4D is promoted to the PS invariant action in 4D. In the gaugino mediation mechanism, the SO(10) gauge multiplet is transmitted to the PS brane through the gaugino mediation with bulk gauge multiplet. Further breaking of the PS gauge group to the SM group is realized by VEVs of the Higgs multiplets (4, 1, 2) ⊕ (4, 1, 2). We show that this model not only cures all pathologies in SO(10) GUT in 4D but also provides the consistent inflation scenario and dark matter candidate and leptogenesis. The gauge coupling unification is successfully realized at ...

Order and anarchy hand in hand in 5D SO(10)

“…There are several SO(10) models, in both renormalizable [25][26][27][28][29][30][31][32][33][34][35][36][37][38] and nonrenormalizable [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] versions (see [56,57] for reviews), where new ingredients are added either to reduce the number of free parameters or to reduce their relevant range. In the first case the predictability of the model is increased, while in the second case the model becomes more natural.…”

Bosonic structure of realistic SO(10) supersymmetric cosmic strings

“…We focus on a well-studied SO(10) SUSY GUT, which has already been considered in a particle physics [15][16][17][18][19][20][21][22]24] and a cosmological [23,25] framework. The superpotential yields [19,32,33] (1) where Σ and Σ are in the 126 and 126 representations, Φ is in the 210 representation, and the inflaton S is a singlet of SO (10).…”

Confronting four zero neutrino Yukawa textures with N2 -dominated leptogenesis

“…Such GUT requirements are inspired by the Yukawa structure of GUT SO(10) models. In a minimal GUT SO(10) setup [66], one assigns all the matter fields including RH neutrinos to the 16 spinor representation of SO(10), while two Higgs fields are found to be in the 10 and 126 representations. Due to the Yukawa interactions (16 16…”