An Algebraic Formulation of Level One Wess-Zumino-Witten Models

Details An Algebraic Formulation of Level One Wess-Zumino-Witten Models An Algebraic Formulation of Level One Wess-Zumino-Witten Models

1995-07-07

arxiv.org/abs/hep-th/9507047v1

Rev.Math.Phys. 8 (1996) 925-948

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, latex2e

Scientific paper

The highest weight modules of the chiral algebra of orthogonal WZW models at level one possess a realization in fermionic representation spaces; the Kac-Moody and Virasoro generators are represented as unbounded limits of even CAR algebras. It is shown that the representation theory of the underlying even CAR algebras reproduces precisely the sectors of the chiral algebra. This fact allows to develop a theory of local von Neumann algebras on the punctured circle, fitting nicely in the Doplicher-Haag-Roberts framework. The relevant localized endomorphisms which generate the charged sectors are explicitly constructed by means of Bogoliubov transformations. Using CAR theory, the fusion rules in terms of sector equivalence classes are proven.

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