Conformal E-infinity theory, exceptional Lie groups and the elementary particle content of the standard model

We begin with Klein's original modular space Gamma(7) for which D = Dim Gamma(7) = |SL(2, 7) = 336. Subsequent compacification D = 336 double right arrow D-c = D + 16k similar or equal to 339 and conformal transformation leads to D-c congruent to 339 double right arrow D-com = (D-c)(1/phi) similar or equal to 548. We observe that this result is identical to summing over all dimensions of the exceptional Lie symmetry groups hierarchy G(2), F-4, E-6, E-7 and E-8 and adding A(1), A(2) and the standard model SM gauge boson to the result. The means Sigma(ex) Dim Lie = |A(1)| + |A(2)| + |G(2)| + |F-4| + |E-6| + |E-7| + |E-8| = 3 + 8 + 14 + 52 + 78 + 133 +248 = 536 and therefore Sigma(ex) Dim Lie + |SM| = 536 + 12 = 548 = D-com. This result is a neat confirmation of the basic group theoretical assumptions of the standard model, namely |SU(3)SU(2) U(1)| = 12 as well as our previous expectation number of the elementary particles in an extended standard model: N(S) = (548 + 4k(0))/8 = (alpha) over bar (0)/2 = 137 + k(0) similar or equal to 69 particles. (C) 2007 Elsevier Ltd. All rights reserved.