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**Nicolai digs back into string theory--supergravity, E8, octonions**

Hermann Nicolai is an interesting researcher to watch for several reasons. He is a leader in theoretical particle physics. Has been on the main advisory committee for the annual Strings conference for the last 10 years or so. A leader in the String community. Knows a lot about non-string QG and various approaches to unification. And when necessary can develop a new, testable, minimalist approach to unification that doesn't require string, or low energy supersymmetry. The kind of person who is recognized good at things you already heard about, but also will sometimes start cutting a path in a completely new direction you hadn't already heard about. So an instructive person to watch.

And for several years he has been working on a non-string program that he worked out with Kris Meissner, the extreme minimalist approach that makes the Standard Model extend out to Planck scale with almost no new concepts. That makes LHC testable predictions and if it were to turn out right it would make a lot of more elaborate theorizing unnecessary. (In that respect it resembles the asymptotic safety approach of Reuter Percacci Weinberg and others).

But just recently Nicolai came out with a string theory paper. And I'm interested to get a sense of what kind of string theory paper it is, and where it is going. So if anyone wants to interpret or comment or explicate for us that would be fine. Here is the paper:

http://arxiv.org/abs/0912.0854

**Cosmological quantum billiards**

Axel Kleinschmidt, Hermann Nicolai

18 pages

(Submitted on 4 Dec 2009)

"The mini-superspace quantization of D=11 supergravity is equivalent to the quantization of a E

_{10}/K(E

_{10}) coset space sigma model, when the latter is restricted to the E

_{10}Cartan subalgebra. As a consequence, the wavefunctions solving the relevant mini-superspace Wheeler-DeWitt equation involve automorphic (Maass wave) forms under the modular group W

^{+}(E

_{10})=PSL

_{2}(Oct).* Using Dirichlet boundary conditions on the billiard domain a general inequality for the Laplace eigenvalues of these automorphic forms is derived, entailing a wave function of the universe that is generically complex and always tends to zero when approaching the initial singularity. The significance of these properties for the nature of singularities in quantum cosmology in comparison with other approaches is discussed. The present approach also offers interesting new perspectives on some long standing issues in canonical quantum gravity"

*The Octonions are used here. The authors use the letter O in a special font to designate the octonions. Here I have substituted the abbreviation "Oct" to make their abstract more immediately understandable.

E

_{10}is related to the exceptional Lie group E

_{8}used by Garrett Lisi and many other people. The official name of E

_{10}is the hyperbolic Kac-Moody group. It is described as an infinite dimensional extension of E

_{8}.

I gather that SL(2, Oct) or alternatively written SL

_{2}(Oct) would be the octonion analog of SL(2, C) which is the 2x2 matrices of complex numbers, with determinant equal one. In effect you just take those 2x2 matrices and substitute in octonions instead of complex numbers.

And SL(2, C) is familiar to many people as a stand-in for the Lorentz group, the transformations used in special relativity. So SL(2, Oct) could be a weirded-up version of the Lorentz group.

What I am hoping, or part of what I'm hoping, is that Garrett will comment.

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