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

Abstract

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 $k+2\ne 0$ and isospin values of the type $J=j-j^{\prime }(k+2)$, $2j,2j^{\prime }\in Z{Z}_{+}$.

40 pages

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