Topological Grand Unification

The grand unification is an attractive idea and offers unification of forces and (partial) unification of quarks and leptons in each family.1) For the gauge bosons and the weak Higgs doublet in the standard model (SM), extra gauge bosons and colored Higgs boson are necessary to form complete multiplets of a unified gauge group, GU . Extra particles and their superpartners cause severe problems as if they came from Pandora’s box. The typical ones are the proton decay problem (why is the proton so stable?)2) and the triplet-doublet Higgs mass splitting problem (how is the Higgs mass splitting realized without fine-tuning among parameters?)∗∗), in the minimal supersymmetric extension of grand unified theory (SUSY GUT).3) The root of all evils stems from the existence of extra heavy particles which generate physical effects, and hence we come across the conjecture that the proton stability and the triplet-doublet Higgs mass splitting can be realized compatible with the grand unification, if extra particles were unphysical and did not affect any physical processes. In other words, the gauge coupling unification originates from a unified gauge symmetry in a high-energy scale and fields are GU -multiplets. If some of them had unphysical degrees of freedom, the full symmetry would not be realized in the physical world. Then physical fields can be the multiples of the SM gauge group, GSM, and survive in the low-energy scale, where the SM particles (and their superpartners) play an essential role. Unphysical modes would be eliminated by a big local symmetry such as a topological symmetry11)and a dynamics. In this paper, we propose a new grand unification scenario to guarantee the proton stability and the triplet-doublet Higgs mass splitting on the basis of the above conjecture. We give simple models with SU(5) gauge group on a space-time including extra superspace to realize our proposal. The reduction to the SM or the minimal supersymmetric SM (the MSSM) is carried out by making use of ParisiSourlas mechanism.12) This paper is organized as follows. In the next section, we elaborate our scenario. In §3, we construct simple models to materialize our scenario. Section 4 is devoted