@inproceedings{2a4801a83400421c8c044c6c4b0bc356,

title = "Quasiconformal Teichmueller theory as an analytical foundation for two-dimensional conformal field theory",

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.",

keywords = "Conformal Field Theory, Teichm{\"u}ller theory, Quasiconformal mapping",

author = "David Radnell and Eric Schippers and Wolfgang Staubach",

year = "2017",

language = "English",

isbn = "978-1-4704-2666-8",

series = "Contemporary Mathematics",

publisher = "AMERICAN MATHEMATICAL SOCIETY",

pages = "205--238",

editor = "Katrina Barron and Elizabeth Jurisich and Antun Milas and Kailash Misra",

booktitle = "Lie Algebras, Vertex Operator Algebras, and Related Topics",

address = "United States",

note = "Lie Algebras, Vertex Operator Algebras, and Related Topics ; Conference date: 14-08-2015 Through 18-08-2015",

}