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BKL dimensional reduction

  1. Aug 28, 2010 #1


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    Carlip has argued that the dimensional reduction in many apprroaches to quantum gravity is related to the BKL limit where the dynamics becomes 1D, and the spectral dimension becomes 2D. http://arxiv.org/abs/0909.3329

    Interestingly, another viewpoint about the (de)-emergence of space comes from Damour and Nicolai also via studying the BKL limit. Related?

    Symmetries,Singularities and the De-Emergence of Space
    Thibault Damour, Hermann Nicolai
    Recent work has revealed intriguing connections between a Belinsky-Khalatnikov-Lifgarbagez-type analysis of spacelike singularities in General Relativity and certain infinite dimensional Lie algebras, and in particular the `maximally extended' hyperbolic Kac--Moody algebra E10. In this essay we argue that these results may lead to an entirely new understanding of the (quantum) nature of space(-time) at the Planck scale, and hence -- via an effective `de-emergence' of space near a singularity -- to a novel mechanism for achieving background independence in quantum gravity.
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  3. Aug 28, 2010 #2


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    Some reviews. The first is in Living Reviews, the others are masters and doctoral theses.

    Spacelike Singularities and Hidden Symmetries of Gravity
    Marc Henneaux, Daniel Persson, Philippe Spindel

    Algebraic structures in M-theory
    Ling Bao

    Kac-Moody Algebras in M-theory
    Sophie de Buyl

    Connections between Kac-Moody algebras and M-theory
    Paul P. Cook

    Kac-Moody algebraic structures in supergravity theories
    Nassiba Tabti

    Exceptional Lie algebras and M-theory
    Jakob Palmkvist

    Arithmetic and Hyperbolic Structures in String Theory
    Daniel Persson
    Last edited: Aug 28, 2010
  4. Apr 5, 2012 #3


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    Dearly Missed

    I was recently reminded of this 2007 paper which you called attention to. What jogged my memory is the abstract of the talk (just posted) that Nicolai will be giving in July of this year at the Stockholm Marcel Grossman (MG13) meeting.
    Let me get the abstract of his MG13 talk.
    The MG13 website has now posted 14 abstracts of the invited plenary talks including this one:

    Hidden symmetries: from BKL to Kac-Moody
    ABSTRACT: The seminal work of Belinski, Khalatnikov and Lifgarbagez on spacelike singularities in cosmological solutions of Einstein's equations has not only generated a new paradigm in General Relativity, but may also provide important hints as to the underlying symmetries of a future unified theory of the fundamental interactions and of quantum gravity. In this talk I will briefly retrace the steps from their early work to more recent developments.

    I can't find any recent papers by Nicolai that seemed to correspond to this talk and I'm curious. Did I miss something obvious? Does anybody know of any current research that could give a clue as to the content of this talk?
    Last edited: Apr 5, 2012
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