In this paper we suggest a new model of preons–dyons making composite quark–leptons and bosons, described by the supersymmetric string-inspired flipped [Formula: see text] gauge group of symmetry. This approach predicts the possible extension of the Standard Model to the family replicated gauge group model of type GN fam , where N fam is the number of families and G is the symmetry group: G = SMG, SU(5), SO(10), E6, etc. Here E6 and [Formula: see text] are nondual and dual sectors of theory with hyperelectric g and hypermagnetic [Formula: see text] charges, respectively. Starting with an idea that the most realistic model leading to the unification of all fundamental interactions (including gravity) is the "heterotic" string-derived flipped model, we have assumed that at high energies μ > 1016 GeV there exists the following chain of the flipped models: [Formula: see text] ended by the flipped E6 gauge group of symmetry at the scale M SSG ~ 1018 GeV . Suggesting N = 1 supersymmetric [Formula: see text] preonic model we have considered preons as dyons confined by hypermagnetic strings in the region of energies μ≲M Pl . Our model is based on the recent theory of composite non-Abelian flux tubes in SQCD — analog ANO-strings. Considering the breakdown of E6 and [Formula: see text] at the Planck scale into the SU(6) × U(1) gauge group, we have shown that the six types of k-strings — composite N = 1 supersymmetric non-Abelian flux tubes — are created by the condensation of spreons–dyons near the Planck scale and have six fluxes quantized according to the Z6 center group of SU(6): Φn = nΦ0(n = ±1, ±2, ±3). These fluxes give three types of k-strings with tensions Tk = kT0, where k = 1, 2, 3, and produce three (and only three) generations of composite quark–leptons and bosons giving a very specific type of "horizontal symmetry." Thus, the present model predicts N gen = N fam = 3. It was shown that our preonic strings are very thin, with radius R str ~ 10-18 GeV -1, and their tension T0 is enormously large: T0 ~ 1038 GeV 2. It was shown that the condensation of spreons near the Planck scale gives the phase transition at some scales M crit and [Formula: see text], which correspond to the following breakdowns of E6 (or [Formula: see text]) for preons: E6 →SU(6)×U(1), or [Formula: see text]. We have calculated the critical values of gauge coupling constants: α-1(M crit ) ≈4.23 and [Formula: see text]. It was investigated that in our world we have quark–leptons and gauge bosons Aμ in the region of energies μ≲M Pl , but monopolic "quark–leptons" and dual gauge fields [Formula: see text] exist in the region μ≳M Pl .
Wormholes and flux tubes in 7D gravity on the principal bundle with the SU(2) gauge group as the extra dimensions