# BKL dimensional reduction

1. Aug 28, 2010

### atyy

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?

http://arxiv.org/abs/0705.2643
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.

2. Aug 28, 2010

### atyy

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

http://arxiv.org/abs/0710.1818
Spacelike Singularities and Hidden Symmetries of Gravity
Marc Henneaux, Daniel Persson, Philippe Spindel

http://arxiv.org/abs/hep-th/0604145
Algebraic structures in M-theory
Ling Bao

http://arxiv.org/abs/hep-th/0608161
Kac-Moody Algebras in M-theory

http://arxiv.org/abs/0711.3498
Connections between Kac-Moody algebras and M-theory
Paul P. Cook

http://arxiv.org/abs/0910.1444
Kac-Moody algebraic structures in supergravity theories
Nassiba Tabti

http://arxiv.org/abs/0912.1612
Exceptional Lie algebras and M-theory
Jakob Palmkvist

http://arxiv.org/abs/1001.3154
Arithmetic and Hyperbolic Structures in String Theory

Last edited: Aug 28, 2010
3. Apr 5, 2012

### marcus

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:
http://www.icra.it/MG/mg13/invited_speakers_details.htm#nicolai

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