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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

### Standard

**Quasiconformal Teichmueller theory as an analytical foundation for two-dimensional conformal field theory.** / Radnell, David; Schippers, Eric; Staubach, Wolfgang.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

### Harvard

*Lie Algebras, Vertex Operator Algebras, and Related Topics: Conference in honor of J. Lepowsky and R. Wilson, August 14-18, 2015, University of Notre Dame, Notre Dame, Indiana.*Contemporary Mathematics, vol. 695, pp. 205-238, Lie Algebras, Vertex Operator Algebras, and Related Topics, Notre Dame, United States, 14/08/2015.

### APA

*Lie Algebras, Vertex Operator Algebras, and Related Topics: Conference in honor of J. Lepowsky and R. Wilson, August 14-18, 2015, University of Notre Dame, Notre Dame, Indiana*(pp. 205-238). (Contemporary Mathematics; Vol. 695).

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TY - GEN

T1 - Quasiconformal Teichmueller theory as an analytical foundation for two-dimensional conformal field theory

AU - Radnell, David

AU - Schippers, Eric

AU - Staubach, Wolfgang

PY - 2017

Y1 - 2017

N2 - 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 conformalfield 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.

AB - 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 conformalfield 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.

KW - Conformal Field Theory

KW - Teichmüller theory

KW - Quasiconformal mapping

UR - http://www.ams.org/books/conm/695/

M3 - Conference contribution

SN - 978-1-4704-2666-8

T3 - Contemporary Mathematics

SP - 205

EP - 238

BT - Lie Algebras, Vertex Operator Algebras, and Related Topics

A2 - Barron, Katrina

A2 - Jurisich, Elizabeth

A2 - Milas, Antun

A2 - Misra, Kailash

ER -

ID: 14696594