Solutions of the Knizhnik - Zamolodchikov Equation with Rational Isospins and the Reduction to the Minimal Models

Details Solutions of the Knizhnik - Zamolodchikov Equation with Rational Isospins and the Reduction to the Minimal Models Solutions of the Knizhnik - Zamolodchikov Equation with Rational Isospins and the Reduction to the Minimal Models

1992-01-31

arxiv.org/abs/hep-th/9201080v1

Nucl.Phys. B394 (1993) 665-706

Physics

High Energy Physics

High Energy Physics - Theory

40 pages

Scientific paper

10.1016/0550-3213(93)90227-G

In the spirit of the quantum Hamiltonian reduction we establish a relation between the chiral $n$-point functions, as well as the equations governing them, of the $A_1^{(1)}$ WZNW conformal theory and the corresponding Virasoro minimal models. The WZNW correlators are described as solutions of the Knizhnik - Zamolodchikov equations with rational levels and isospins. The technical tool exploited are certain relations in twisted cohomology. The results extend to arbitrary level $k+2 \neq 0$ and isospin values of the type $J=j-j'(k+2)$, $ \ 2j, 2j' \in Z\!\!\!Z_+$.

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