Hermann Nicolai's talk was very interesting.
http://www.ift.uni.wroc.pl/~planckscale/movie/
It covered work on a possible way of extending the Standard Model all the way to Planck scale with a minimum of complications---stressing econony. Work with Kris Meissner, one of the two people who organized the conference.
http://arxiv.org/abs/0710.2840
Effective Action, Conformal Anomaly and the Issue of Quadratic Divergences
Krzysztof A. Meissner, Hermann Nicolai
17 pages
(Submitted on 15 Oct 2007)
"For massless phi
4 theory, we explicitly compute the lowest order non-local contributions to the one-loop effective action required for the determination of the trace anomaly. Imposing exact conformal invariance of the local part of the effective action, we argue that the issue of quadratic divergences does not arise in a theory where exact conformal symmetry is only broken by quantum effects. Conformal symmetry can thus replace low energy supersymmetry as a possible guide towards stabilizing the weak scale and solving the hierarchy problem, if (i) there are no intermediate scales between the weak scale and the Planck scale, and (ii) the running couplings exhibit neither Landau poles nor instabilities over this whole range of energies."
http://arxiv.org/abs/0803.2814
Neutrinos, Axions and Conformal Symmetry
Krzysztof A. Meissner, Hermann Nicolai
10 pages, 2 figures, Eur.Phys.J.C57:493-498,2008
(Submitted on 19 Mar 2008)
"We demonstrate that radiative breaking of conformal symmetry (and simultaneously electroweak symmetry) in the Standard Model with right-chiral neutrinos and a minimally enlarged scalar sector induces spontaneous breaking of lepton number symmetry, which naturally gives rise to an axion-like particle with some unusual features. The couplings of this 'axion' to Standard Model particles, in particular photons and gluons, are entirely determined (and computable) via the conformal anomaly, and their smallness turns out to be directly related to the smallness of the masses of light neutrinos."
http://arxiv.org/abs/0809.1338
Renormalization Group and Effective Potential in Classically Conformal Theories
Krzysztof A. Meissner, Hermann Nicolai
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."
http://arxiv.org/abs/0907.3298
Conformal invariance from non-conformal gravity
Krzysztof A. Meissner, Hermann Nicolai
(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."
Suppose you wanted to choose three talks that could serve to "triangulate" the current main direction of the effort to formulate Planckscale models of geometry and matter. To extend both the Standard Model and General Relativity to high energy density/small scale. What recent lectures would you choose?
I think I would pick:
Steve Carlip ( 29 June at the Planck Scale conference)
Hermann Nicolai (also 29 June at the Planck Scale conference)
Steven Weinberg (7 July at Cern)
For Weinberg start at minute 58 of this talk:
http://cdsweb.cern.ch/record/1188567/ or watch the first 58 minutes as well, for history and context.
The other two are at:
http://www.ift.uni.wroc.pl/~planckscale/movie/