English

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

Quantum Algebra 2007-05-23 v1 Mathematical Physics Algebraic Geometry math.MP

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.

Keywords

Cite

@article{arxiv.math/0001040,
  title  = {Elements of a Global Operator Approach to Wess-Zumino-Novikov-Witten Models},
  author = {Martin Schlichenmaier},
  journal= {arXiv preprint arXiv:math/0001040},
  year   = {2007}
}

Comments

17 pages, Amslatex, Invited talk presented at the 3rd International Workshop on "Lie Theory and Its Applications in Physics - Lie III", 11 - 14 July 1999, Clausthal, Germany