Geometric construction of modular functors from Conformal Field Theory

Abstract

This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [TUY] by a certain fractional power of the abelian theory first considered in [KNTY] and further studied in our first paper [AU1].

Paper considerably expanded so as to make it self contained

References in corpus (2)

• Abelian Conformal Field theories and Determinant Bundles
• Finite-Dimensionality of the Space of Conformal Blocks

Cited by in corpus (20)

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• The Witten-Reshetikhin-Turaev invariant for links in finite order mapping tori I
• String Topology: Background and Present State
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• From WZW models to Modular Functors
• Hitchin's Connection in Half-Form Quantization
• Mapping class group invariant unitarity of the Hitchin connection over Teichmüller space
• A Geometric Quantisation view on the AJ-conjecture for the Teichmüller TQFT
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• Modular functors with infinite dimensional Hilbert spaces