Are preons dyons? Naturalness of three generations

In the present paper a model of preons and their composites is constructed in the framework of the superstring-inspired flipped E₆×E˜₆ gauge symmetry group which reveals a generalized dual symmetry. Here E₆ and E˜₆ are nondual and dual sectors of the theory with hyperelectric g and hypermagnetic g˜ charges, respectively. We follow the old idea by J. Pati presuming that preons are dyons, which in our model are confined by hyper-magnetic strings—composite N=1 supersymmetric non-Abelian flux tubes created by the condensation of spreons near the Planck scale. Considering preons belonging to the 27-plet of E₆, we have investigated the breakdown of E₆ (and E˜₆) near the Planck scale into the SU(6)× U(1) (and SU(6)˜×U(1)˜) gauge group and shown that the six types of strings having fluxes Φ_n=nΦ₀ (n=±1,±2,±3) produce three (and only three) generations of composite quark-leptons and bosons. The model predicts the existence of the Family replicated gauge group [E₆]³ near the Planck scale. The runnings of the corresponding fine structure constants are investigated, and the critical coupling constants at the two phase transition points near the Planck scale are calculated. The model explains the hierarchies of masses in the standard model naturally. The compactification in a space-time with five dimensions and its influence on form-factors of composite objects are also briefly discussed.