Quasiconformal Teichmüller theory as an analytical foundation for two dimensional conformal field theory
(English)In: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627Article in journal (Refereed) Accepted
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 Teichmüller 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.
Geometry Mathematical Analysis Other Physics Topics
IdentifiersURN: urn:nbn:se:uu:diva-284595OAI: oai:DiVA.org:uu-284595DiVA: diva2:920685