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arXiv · hep-th/0301181

Lie algebras, Fuchsian differential equations and CFT correlation functions

Jürgen Fuchs·Ingo Runkel·Christoph Schweigert
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Abstract

Affine Kac-Moody algebras give rise to interesting systems of differential equations, so-called Knizhnik-Zamolodchikov equations. The monodromy properties of their solutions can be encoded in the structure of a modular tensor category on (a subcategory of) the representation category of the affine Lie algebra. We discuss the relation between these solutions and physical correlation functions in two-dimensional conformal field theory. In particular we report on a proof for the existence of the latter on world sheets of arbitrary topology.

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Jürgen Fuchs, Ingo Runkel, Christoph Schweigert. 2003-01-23. Lie algebras, Fuchsian differential equations and CFT correlation functions. https://arxiv.org/abs/hep-th/0301181

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