Generalization of the Knizhnik-Zamolodchikov-Equations

Details Generalization of the Knizhnik-Zamolodchikov-Equations Generalization of the Knizhnik-Zamolodchikov-Equations

1996-10-09

arxiv.org/abs/hep-th/9610066v1

Lett.Math.Phys. 41 (1997) 169-180

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, uses amssymb

Scientific paper

In this letter we introduce a generalization of the Knizhnik- Zamolodchikov equations from affine Lie algebras to a wide class of conformal field theories (not necessarily rational). The new equations describe correlations functions of primary fields and of a finite number of their descendents. Our proposal is based on Nahm's concept of small spaces which provide adequate substitutes for the lowest energy subspaces in modules of affine Lie algebras. We explain how to construct the first order differential equations and investigate properties of the associated connections, thereby preparing the grounds for an analysis of quantum symmetries. The general considerations are illustrated in examples of Virasoro minimal models.

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