Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-04-09
J.Geom.Phys. 56 (2006) 55-85
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, LaTeX. To appear in Journal of Geometry and Physics
Scientific paper
This is a survey of our results on the relation between perturbative renormalization and motivic Galois theory. The main result is that all quantum field theories share a common universal symmetry realized as a motivic Galois group, whose action is dictated by the divergences and generalizes that of the renormalization group. The existence of such a group was conjectured by P. Cartier based on number theoretic evidence and on the Connes-Kreimer theory of perturbative renormalization. The group provides a universal formula for counterterms and is obtained via a Riemann-Hilbert correspondence classifying equivalence classes of flat equisingular bundles, where the equisingularity condition corresponds to the independence of the counterterms on the mass scale.
Connes Alain
Marcolli Matilde
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