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Holographic dimensional reduction: Center manifold theorem and E-infinity

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  • El Naschie, M.S.

Abstract

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.

Suggested Citation

  • El Naschie, M.S., 2006. "Holographic dimensional reduction: Center manifold theorem and E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 816-822.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:4:p:816-822
    DOI: 10.1016/j.chaos.2006.01.013
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    References listed on IDEAS

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    1. El Naschie, M.S., 2005. "On a class of fuzzy Kähler-like manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 257-261.
    2. Iovane, G., 2006. "Cantorian spacetime and Hilbert space: Part I—Foundations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 857-878.
    3. El Naschie, M.S., 2006. "Superstring theory: What it cannot do but E-infinity could," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 65-68.
    4. El Naschie, M.S., 2005. "A guide to the mathematics of E-infinity Cantorian spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 955-964.
    5. El Naschie, M.S., 2006. "Superstrings, entropy and the elementary particles content of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 48-54.
    6. El Naschie, M.S., 2006. "Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 297-330.
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