Proposes that the group completion of planar configuration spaces, equivalent to ΩS^2, is a moduli space whose Jordan-curve states encode renormalized Feynman integrals as residues.
A Perspective on Regularization and Curvature
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abstract
A global connection on the Connes Marcolli renormalization bundle relates $\beta$-functions of a class of regularization schemes by gauge transformations, as well as local solutions to $\beta$-functions over curved space-time.
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Some very low-dimensional algebraic topology
Proposes that the group completion of planar configuration spaces, equivalent to ΩS^2, is a moduli space whose Jordan-curve states encode renormalized Feynman integrals as residues.