2016/05/02 by David Radnell, Eric Schippers, Radnell, David +3
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #math-ph #math.CV #math.MP #msc:30C55 #msc:30C62 #msc:30F60 #msc:32G15 #msc:46E20 #msc:81T40
paper · pdf · doi:10.48550/arxiv.1605.00449
27 pages. Typos fixed and references updated
arxiv created 2017/06/08 · arxiv updated 2017/06/09
The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and the sewing operation. We survey the recent and careful study of these objects, which has led to significant connections with quasiconformal Teichmuller theory and geometric function theory. In particular we propose that the natural analytic setting for conformal field theory is the moduli space of Riemann surfaces with so-called Weil-Petersson class parametrizations. A collection of rigorous analytic results is advanced here as evidence. This class of parametrizations has the required regularity for CFT on one hand, and on the other hand are natural and of interest in their own right in geometric function theory.