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

Radnell, David; Schippers, Eric; Staubach, Wolfgang

doi:10.1090/conm/695/14003

Cited by 12 publications

(10 citation statements)

References 41 publications

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“…The future solution of this problem will depend on the further study of the moduli space of Riemann surfaces with parametrized boundaries, including in particular the study of a conjecture by the author on meromorphic functions on this moduli space. See [RS1]- [RS3] and [RSS1]- [RSS5] for results on this moduli space.…”

Section: A Program To Construct Conformal Field Theoriesmentioning

confidence: 99%

Representation theory of vertex operator algebras and orbifold conformal field theory

Huang¹

2020

Preprint

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We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories. We also clarify some misunderstandings on vertex operator algebras, modular functors and intertwining operator algebras. Then we discuss some basic open problems and conjectures in mathematical orbifold conformal field theory. Generalized twisted modules and their variants, their constructions and some existence results are reviewed. Twisted intertwining operators and their basic properties are also reviewed. The conjectural properties in the basic open problems and conjectures mentioned above are then formulated precisely and explicitly. Some thoughts of the author on further developments of orbifold conformal field theory are also discussed.

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Section: A Program To Construct Conformal Field Theoriesmentioning

confidence: 99%

Representation theory of vertex operator algebras and orbifold conformal field theory

Huang¹

2020

Preprint

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“…These are required for the construction of two-dimensional conformal field theory from vertex operator algebras. A comprehensive review can be found in [52]. The sewing technique is also of independent interest in Teichmüller theory.…”

Section: 4mentioning

confidence: 99%

Comparison Moduli Spaces of Riemann Surfaces

Schippers

Staubach

2017

Trends in Mathematics

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We define a kind of moduli space of nested surfaces and mappings, which we call a comparison moduli space. We review examples of such spaces in geometric function theory and modern Teichmüller theory, and illustrate how a wide range of phenomena in complex analysis are captured by this notion of moduli space. The paper includes a list of open problems in classical and modern function theory and Teichmüller theory ranging from general theoretical questions to specific technical problems.

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“…This can be thought of as a characterization of the possible Fourier series on S 1 obtained by pulling back elements of D(Σ). This characterization relates to the so-called Segal-Wilson Grassmannian, and has applications to two-dimensional conformal field theory and to Teichmüller theory, see D. Radnell, E. Schippers and W. Staubach [14,15].…”

Section: Introductionmentioning

confidence: 99%

Dirichlet spaces of domains bounded by quasicircles

Radnell

Schippers

Staubach

2019

Commun. Contemp. Math.

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Consider a multiply-connected domain Σ in the sphere bounded by n nonintersecting quasicircles. We characterize the Dirichlet space of Σ as an isomorphic image of a direct sum of Dirichlet spaces of the disk under a generalized Faber operator. This Faber operator is constructed using a jump formula for quasicircles and certain spaces of boundary values.Thereafter, we define a Grunsky operator on direct sums of Dirichlet spaces of the disk, and give a second characterization of the Dirichlet space of Σ as the graph of the generalized Grunsky operator in direct sums of the space H 1/2 (S 1 ) on the circle. This has an interpretation in terms of Fourier decompositions of Dirichlet space functions on the circle.

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

Cited by 12 publications

References 41 publications

Representation theory of vertex operator algebras and orbifold conformal field theory

Representation theory of vertex operator algebras and orbifold conformal field theory

Comparison Moduli Spaces of Riemann Surfaces

Dirichlet spaces of domains bounded by quasicircles

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