GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY

2003/06/30 by Jørgen Ellegaard Andersen, Jorgen Ellegaard Andersen, Kenji Ueno · 1 citation
Mathematics · #Abelian category #Abelian group #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Conformal field theory #Conformal map #Construct (python library) #Field (mathematics) #Functor #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Modular design #Pure mathematics #Simple (philosophy) #math.DG #math.QA

paper · pdf · doi:10.1142/s0218216507005233

published as J.KnotTheor.Ramifications16:127-202,2007 · Paper considerably expanded so as to make it self contained

arxiv created 2006/11/08 · openalex publication_date 2007/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16, 19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].

Citations

• Complex Manifolds and Deformation of Complex Structures
• Finite-Dimensionality of the Space of Conformal Blocks
• The analytic geometry of two-dimensional conformal field theory
• Current algebra and Wess-Zumino model in two dimensions
• Quantum field theory and the Jones polynomial
• The irreducibility of the space of curves of given genus

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