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 E8 ⊗ E8 theory corresponds to a fuzzy Kähler manifold with b2-=19-ϕ6 and b2+=5+ϕ3, while the boundary theory of the Γc(7) Klein modular space corresponds to another fuzzy Kähler manifold with b2-=13-ϕ6 and b2+=3-ϕ6. Based on these results, we conclude that the ε(∞) − Γc(7) theory represents a worked out example for the correctness of the holographic principle first proposed by G. ‘t Hooft.