Holographic dimensional reduction:: Center manifold theorem and E-infinity

Klein modular curve is shown to be the holographic boundary of E-infinity Cantorian spacetime. The conformal relation between the full dimensional and the reduced space is explored. We show that both spaces analyzed in the appropriate manner give the same results for certain aspects of high energy particle physics and quantum gravity. Similarity with the center manifold theorem of non-linear dynamics and the theory of bifurcating vector fields is discussed. In particular it was found that the transfinite version of the E-8 circle times E-8 theory corresponds to a fuzzy Kahler manifold with b(2)(-) = 19 - phi(6) and b(2)(+) = 5 + phi(3), while the boundary theory of the Gamma(c)(7) Klein modular space corresponds to another fuzzy Kahler manifold with b(2)(-) = 13 phi(6) and b(2)(+) = 3 phi(6). Based on these results, we conclude that the epsilon((infinity)) - Gamma(c)(7) theory represents a worked out example for the correctness of the holographic principle first proposed by G. 't Hooft. (c) 2006 Elsevier Ltd. All rights reserved.