Quasiconformal Teichmueller theory as an analytical foundation for two-dimensional conformal field theory

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Details

Original languageEnglish
Title of host publicationLie Algebras, Vertex Operator Algebras, and Related Topics
Subtitle of host publicationConference in honor of J. Lepowsky and R. Wilson, August 14-18, 2015, University of Notre Dame, Notre Dame, Indiana
EditorsKatrina Barron, Elizabeth Jurisich, Antun Milas, Kailash Misra
Publication statusPublished - 2017
MoE publication typeA4 Article in a conference publication
EventLie Algebras, Vertex Operator Algebras, and Related Topics - University of Notre Dame, Notre Dame, United States
Duration: 14 Aug 201518 Aug 2015

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society
Volume695

Conference

ConferenceLie Algebras, Vertex Operator Algebras, and Related Topics
CountryUnited States
CityNotre Dame
Period14/08/201518/08/2015

Researchers

Research units

  • University of Manitoba
  • Uppsala University

Abstract

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.

    Research areas

  • Conformal Field Theory, Teichmüller theory, Quasiconformal mapping

ID: 14696594