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Here are five papers by Kris Meissner and Hermann Nicolai:

http://arxiv.org/find/grp_physics/1/AND+au:+Nicolai_H+au:+Meissner/0/1/0/all/0/1

The latest contains a conjecture which they summarize in the concluding paragraph:

"The main conjecture put forward in this paper can therefore be summarized as follows: the hierarchy problem can conceivably be solved via ‘anomalous’ logarithmic quantum corrections in a UV ﬁnite theory of quantum gravity, if the latter admits a ﬂat space limit which is classically conformally invariant. The mass spectrum and pattern of couplings observed in elementary particle physics could then have their origin in quantum gravity."

The background for this latest paper was presented in a talk at the June 2009 Planck Scale conference. It's a good clear talk and can be strongly recommended. The video is here:

http://www.ift.uni.wroc.pl/~rdurka/planckscale/index-video.php?plik=http://panoramix.ift.uni.wroc.pl/~planckscale/video/Day1/1-3.flv&tytul=1.3%20Nicolai [Broken]

The latest paper builds on two earlier Meissner Nicolai papers

http://arxiv.org/abs/hep-th/0612165

Conformal Symmetry and the Standard Model

13 pages, 6 figures, published in Phys. Lett. B

(Submitted on 15 Dec 2006)

"We re-examine the question of radiative symmetry breaking in the standard model in the presence of right-chiral neutrinos and a minimally enlarged scalar sector. We demonstrate that, with these extra ingredients, the hypothesis of classically unbroken conformal symmetry, besides naturally introducing and stabilizing a hierarchy, is compatible with all available data; in particular, there exists a set of parameters for which the model may remain viable even up to the Planck scale. The decay modes of the extra scalar field provide a unique signature of this model which can be tested at LHC."

http://arxiv.org/abs/0809.1338

Renormalization Group and Effective Potential in Classically Conformal Theories

17 pages, 2 figures

(Submitted on 8 Sep 2008)

"We derive a general formula for the RG improved effective (Coleman-Weinberg) potential for classically conformal models, applying it to several examples of physical interest, and in particular a model of QCD coupled via quarks to a colorless scalar field. The closed form expressions allow us to discuss the range of validity of the effective potential as well as the issue of 'large logarithms' in a way different from previous such analyses. Remarkably, in all examples considered, convexity of the effective potential is restored by the RG improvement, or otherwise the potential becomes unstable. In the former case, symmetry breaking becomes unavoidable due to the appearance of an infrared barrier [tex]\Lambda_{IR}[/tex], which hints at a so far unsuspected link between [tex]\Lambda_{QCD}[/tex] and the scale of electroweak symmetry breaking."

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My comment is that we are looking at an idea of a ToE (maybe not by your standards but by mine) unifying and extending to Planck scale. A key part of the construct is testable at LHC.

Another key part is a UV finite 4D quantum theory of gravity, which we don't have yet. But we have signs of such a development---like Reuter AsymSafe and Loll CDT to mention just two. It's possible the bugs will be worked out.

The most recent M-and-N paper ( http://arxiv.org/abs/0907.3298 ) provides what they call an "existence proof" by showing that the idea can be implemented in a case of N=4 supergravity.

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# Meissner Nicolai conjecture-opening to a 4D ToE

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