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

Schlichenmaier, Martin

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URL: http://ub-madoc.bib.uni-mannheim.de/1331
URN: urn:nbn:de:bsz:180-madoc-13314
Document Type: Working paper
Year of publication: 2000
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Abstract: 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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