Alain Connes' Standard Model

Last Thursday Alain Connes gave a talk at CERN TH. Alain is a famous mathematician with important contributions in the areas of operator algebras and non-commutative geometry. He has gathered quite a collection of prestigious awards, including the Fields Medal and the Crafoord Prize. What could bring such a figure to a particle theory seminar? He was sharing his views on the elementary interactions in a talk entitled The Standard Model coupled with gravity, the spectral model and its predictions.

Alain's approach to particle physics is orthogonal to that of the particle physics community. Whereas we try to figure out what sort of new physics could be responsible for the weird structures of the Standard Model, he treats those very structures as an indication of the underlying geometry of space-time. This is certainly original, which has its positives and negatives. One one hand, I find it reassuring that people out there are exploring different ways; in the end, it is conceivable that the standard approach will prove terribly wrong. On the other hand, Alain's language can hardly be understood here at CERN. No, he wasn't speaking french ;-) but I quickly got lost in the forest of KO-theory, metric dimensions and spectral triples. I'm not able to review or evaluate any technical details of his work but I would like to share a few remarks anyway.

His program consists in identifying a structure of space-time could give rise to the Standard Model + gravity. He finds the answer is the product of an ordinary spin manifold by a finite noncommutative discrete space of KO-dimension 6 modulo 8 and of metric dimension 0, whatever it means. The discrete space is responsible for the spectrum, symmetries and the interactions of the Standard Model. Most of the Standard Model parameters correspond to the freedom of parametrizing the internal geometry. There are however three constraints:

1. The gauge couplings should be unified at some scale. The unification is rather weird, as there are no exotic gauge bosons, hence no proton decay.
2. There is a relation between the sum of the fermion masses squared and the W mass. In practice, this is a constraint on the top mass, which is roughly obeyed in nature.
3. Finally, there is a prediction for the higgs quartic coupling, which implies the higgs boson mass of order 170 GeV.

Is it possible that his approach will provide new insights into the Standard Model and beyond? Not likely. As far as I understood, the fine structure of space-time has no implications that could be observed at the LHC or in other experiments in foreseeable future. Next, the Standard Model is not a unique system that allows for such a geometrical embedding. Before the neutrino masses were discovered, Alain himself had pursued a different scenario leading to massless neutrinos. In fact, non-unification of the gauge couplings within the Standard Model suggests that there should be more low-energy structures asking for a different space-time geometry. According to Alain, supersymmetry could find a place in this game, too. Thus, his program can hardly constrain the options for the LHC. Even the 170 GeV Higgs mass is sensitive to the assumptions he makes, e.g. to the value of the unification scale. In conclusion, his approach seems more a mathematical re-interpretion of QFT structures than a self-standing physical theory.

In spite of these objections, I really enjoyed the talk. I think it is due to Alain's manner of speaking: a soft voice full of wonder at the mathematical beauty he perceives in his models. One could think he speaks of autumn trees or little birds in nest, not about scaring non-commutative geometry :-) This sort of enthusiam is rare these days.

The transperiences are not available, as usual. For brave souls, the technical details can be found in the recent paper of Alain and collaborators.