Meissner Nicolai conjecture-opening to a 4D ToE

[marcus]

Meissner Nicolai conjecture---opening to a 4D ToE

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

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 $$\Lambda_{IR}$$, which hints at a so far unsuspected link between $$\Lambda_{QCD}$$ 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.

 

[marcus]

So here is their "existence proof" or prototype proof-of-concept paper, where they take N=4 supergravity and show how to proceed. We can think of N=4 supergravity merely as a place-holder, standing in for whatever QG is eventually developed.

Conformal invariance from non-conformal gravity
Krzysztof A. Meissner, Hermann Nicolai
18 pages
(Submitted on 20 Jul 2009)
"We discuss the conditions under which classically conformally invariant models in four dimensions can arise out of non-conformal (Einstein) gravity. As an 'existence proof' that this is indeed possible we show how to derive N=4 super Yang Mills theory with any compact gauge group G from non-conformal gauged N=4 supergravity as a special flat space limit. We stress the role that the anticipated UV finiteness of the (so far unknown) underlying theory of quantum gravity would have to play in such a scheme, as well as the fact that the masses of elementary particles would have to arise via quantum gravitational effects which mimic the conformal anomalies of standard (flat space) UV divergent quantum field theory."

Personally, I begin to be convinced that the Planck Scale 2009 conference should be a model for future conferences, because it brought relativists and particle theorists together in a constructive and informative way. A variety of (non-fanciful, non-baroque) approaches were presented and discussed.
The videos from this conference are unusually helpful. And with each video, there is a downloadable PDF of the slides that you can print out ahead of time to have in hand while watching the video. This is convenient to do in the case of Nicolai's lecture because often the camera is on the speaker and one needs to consult the printout to see what is being projected on the screen.

 

[Entropia]

This is a significant step forward in the development of a 4D ToE, as it provides a concrete example of how the hierarchy problem can be solved within a conformally invariant theory of quantum gravity.

However, as with any conjecture, there is still much work to be done in order to fully understand and validate the Meissner Nicolai conjecture. It will require further theoretical developments and experimental evidence to confirm its validity. But it is a promising area of research and could potentially lead to a deeper understanding of the fundamental laws of nature.

In summary, the Meissner Nicolai conjecture is an intriguing idea that offers a potential solution to the hierarchy problem and a promising avenue for the development of a 4D ToE. While there is still much to be explored and tested, it is a significant step forward in our quest to understand the fundamental nature of our universe.