Preon Model and Family Replicated E₆ Unification

Abstract

Abstract. Previously we suggested a new preon model of composite quark-leptons and bosons with the 'flipped' E 6 × E 6 gauge symmetry group. We assumed that preons are dyons having both hyper-electric g and hyper-magneticg charges, and these preons-dyons are confined by hyper-magnetic strings which are an N = 1 supersymmetric non-Abelian flux tubes created by the condensation of spreons near the Planck scale. In the present paper we show that the existence of the three types of strings with tensions T k = kT 0 (k = 1, 2, 3) producing three (and only three) generations of composite quark-leptons, also provides three generations of composite gauge bosons ('hyper-gluons') and, as a consequence, predicts the family replicated [E 6 ] 3 unification at the scale ∼ 10 17 GeV. This group of unification has the possibility of breaking to the group of symmetry:3 which undergoes the breakdown to the Standard Model at lower energies. Some predictive advantages of the family replicated gauge groups of symmetry are briefly discussed.

Polynomial Representation of E6 and Its Combinatorial and PDE Implications

“…Howl and King [20] proposed a minimal E 6 supersymmetric standard model which allows Planck scale unification, provides a solution to the µ problem and predicts a new Z ′ . Das and Laperashvili [12] studied Preon model related to family replicated E 6 unification.…”

Mapping the geometry of the E6 group

“…This is particularly interesting, because recently it has been argued that this group could be the most promising for unification in GUT theories [3,6]. To parameterize the group we have used the generalized Euler angles method, a technique we introduced in [2,1] to give the most simple expression for the invariant measure on the group, while at the same time still being able to provide an explicit expression for the range of the parameters.…”

“…QQ [7,1] = e [7]; QQ [7,2] = e [6]; QQ [7,3] = −e [8]; QQ [7,4] = e [5]; QQ [7,5] = −e [4]; QQ [7,6] = −e [2]; QQ [7,7] = −e [1]; QQ [7,8] %%%% construction of the matrices MT = { {{mt [1], 0, 0, 0, 0, 0, 0, 0}, {mt [2], mt [3], mt [4], mt [5], mt [6], mt [7], mt [8], mt [9]}, {mt [10], mt [11] C The matrices.…”

“…E.g., it is already known that the current estimate for the lower bound of the proton lifetime rules out some of the GUT models candidates. Recently, the particular structure of the neutrino mixing matrix seems to suggest that a good candidate for a GUT could be based on the semidirect product between the exceptional group E 4 6 and the discrete group S 4 [3,6]. In general, while the local properties of the group G, which for a Lie group are all encoded in the corresponding Lie algebra, are enough to perform a perturbative analysis, in order to obtain non perturbative results, such as instantonic calculations or lattice simulations, a knowledge of the entire group structure is required, in particular of the invariant measure on the group in a suitable global parametrization.…”

“…In our previous paper [1] we determined the algebra of derivations D and used it to obtain an irreducible representation of the exceptional algebra f 4 . To obtain a representation of e 6 we only need to determine the matrix representation of R Y . This is a very simple task and we solved it in R 27 with the product inherited from J 3 by means of the linear isomorphism Φ : J 3 −→ R 27 , A → Φ(A) ,…”