Supersymmetric unification in the light of neutrino mass

We argue that with the discovery of neutrino mass effects at super-Kamiokande there is a clear logical chain leading from the standard model through the MSSM and the recently developed minimal left right supersymmetric models with a renormalizable see-saw mechanism for neutrino mass to left right symmetric SUSY GUTS: in particular, SO(10) and SU(2) _L × SU(2) _R × SU(4) _c . The progress in constructing such GUTS explicitly is reviewed and their testability/falsifiability by proton decay measurements emphasized.     

Supersymmetric family unification

The superheavy symmetry breaking of the gauge group in supersymmetrized unified theories is studied. The requirement that supersymmetry be unbroken strongly constraints the possible gauge group breaking, and we systematize such constraints group theoretically.In model building, one issue is whether to permit an adjoint matter superfield with concomitant color exotic fermions. A second issue is that of naturalness which is complicated by the well-known supersymmetry non-renormalization theorems.Both with and without an adjoint matter superfield, the most promising group appears to be SU(9) where three families can be naturally accommodated, at least for low-energy gauge group SU(3)×SU(20×U(1). With an extra U(1) factor, as advocated by Fayet, the non-renormalization theorem must be exploited.     

Supersymmetric unification at the millennium

We argue that the discovery of neutrino mass effects at super-Kamiokande implies a clear logical chain leading from the Standard Model, through the MSSM and the recently developed minimal left right supersymmetric models with a renormalizable see-saw mechanism for neutrino mass, to left right symmetric SUSY GUTS: in particular, SO(10) and SU(2) _L × SU(2) _R × SU(4) _C . The progress in constructing such GUTS explicitly is reviewed and their testability/falsifiability by lepton flavour violation and proton decay measurements emphasized. SUSY violations of the survival principle and the interplay between third generation Yukawa coupling unification and the structurally stable IR attractive features of the RG flow in SUSY GUTS are also discussed.     

Barygenesis without grand unification

A mechanism is pointed out to generate cosmological baryon number excess without resorting to grand unified theories. The lepton number excess originating from Majorana mass terms may transform into the number excess through the unsuppressed baryon number violation of electroweak processes at high temperatures.     

The geometry of grand unification

Arguments are presented which lead to the conclusion thatSU(3, 2) is the grand unification gauge group (GUGG). The gauge theory includes all known forces. We incorporated supersymmetry within the framework of the gauge theory and show how the theory may be quantized.     

A grand unification of flavour with testable predictions

We present a grand unification of flavour based on the group O (14) = SO(14) ? K'. The novel feature of this model is that the discrete symmetry K' is not the internal parity. This implies a fermion assignment different from the usual O(14) with important consequences on the low energy phenomenology. One new fermion family with V - A weak interactions and four new families with V + A character are predicted, with masses less than 250 GeV. The cosmological bound on light neutrino species forces us to keep an SU(2) family group acting on the V + A families unbroken until low energy. Depending on the hierarchy pattern, either we recover the standard model predictions or a new scenario emerges with substantial departures in the neutral current phenomenology.     

Isotopic grand unification with the inclusion of gravity

We introduce a dual lifting of unified gauge theories, the first characterized by theisotopies, which are axiom-preserving maps into broader structures with positive-definite generalized units used for the representation of matter under the isotopies of the Poincaré symmetry, and the second characterized by theisodualities, which are anti-isomorphic maps with negative-definite generalized units used for the representation of antimatter under the isodualities of the Poincaré symmetry. We then submit, apparently for the first time, a novel grand unification with the inclusion of gravity for matter embedded in the generalized positive-definite units of unified gauge theories while gravity for antimatter is embedded in the isodual isounit. We then show that the proposed grand unification provides realistic possibilities for a resolution of the axiomatic incompatibilities between gravitation and electroweak interactions due to curvature, antimatter and the fundamental space-time symmetries.     

Proton hexality in local grand unification

Proton hexality is a discrete symmetry that avoids the problem of too fast proton decay in the supersymmetric extension of the standard model. Unfortunately it is inconsistent with conventional grand unification. We show that proton hexality can be incorporated in the scheme of “Local Grand Unification” discussed in the framework of model building in (heterotic) string theory.     

SU(8) grand unification

A grand unified gauge theory based on the group SU(8) is presented. The set of rules motivating the choice of SU(8) is given. The particle content of the theory suggests a natural embedding of a horizontal SU(3) symmetry in the SU(8) grand unified symmetry.     

Hierarchical fermion masses from grand unification

A mechanism is presented for generating fermion masses as a reflection of the superheavy fermions existing in a class of grand unified theories. By means of it we propose a way of understanding how, giving a driving mass term for the top-generation, the charm-generation mass results as a relative first-order perturbation in the unified gauge coupling g²/4π ≈ 10^?2, and the up-generation mass as a second-order perturbation. An illustrative calculation of the charm-generation mass is described in a model based on E₆.