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 #Boundary (topology) #Class (philosophy) #Computer science #Conformal field theory #Conformal map #Extremal length #Field (mathematics) #Function (biology) #Geometric function theory #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Moduli space #Pure mathematics #Riemann surface #Space (punctuation) #Teichmüller space #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
published in arXiv (Cornell University) (Cornell University) · 27 pages. Typos fixed and references updated
openalex publication_date 2016/05/02 · arxiv created 2017/06/08 · arxiv updated 2017/06/09 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
The functorial mathematical definition of conformal field theory was first\nformulated approximately 30 years ago. The underlying geometric category is\nbased on the moduli space of Riemann surfaces with parametrized boundary\ncomponents and the sewing operation. We survey the recent and careful study of\nthese objects, which has led to significant connections with quasiconformal\nTeichmuller theory and geometric function theory.\n In particular we propose that the natural analytic setting for conformal\nfield theory is the moduli space of Riemann surfaces with so-called\nWeil-Petersson class parametrizations. A collection of rigorous analytic\nresults is advanced here as evidence. This class of parametrizations has the\nrequired regularity for CFT on one hand, and on the other hand are natural and\nof interest in their own right in geometric function theory.\n