Elements of a Global Operator Approach to Wess-Zumino-Novikov-Witten Models

Details Elements of a Global Operator Approach to Wess-Zumino-Novikov-Witten Models Elements of a Global Operator Approach to Wess-Zumino-Novikov-Witten Models

2000-01-07

arxiv.org/abs/math/0001040v1

Mathematics

Quantum Algebra

17 pages, Amslatex, Invited talk presented at the 3rd International Workshop on "Lie Theory and Its Applications in Physics -

Scientific paper

Elements of a global operator approach to the WZNW models for compact Riemann surfaces of arbitrary genus g with N marked points were given by Schlichenmaier and Sheinman. This contribution reports on the results. The approach is based on the multi-point Krichever-Novikov algebras of global meromorphic functions and vector fields, and the global algebras of affine type and their representations. Using the global Sugawara construction and the identification of a certain subspace of the vector field algebra with the tangent space to the moduli space of the geometric data, Knizhnik-Zamalodchikov equations are defined. Some steps of the approach of Tsuchia, Ueno and Yamada to WZNW models are presented to compare it with our approach.

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