\(SL(N)\) Kac-Moody algebras and Wess-Zumino-Witten models (Q1814302)

The author represents Wess-Zumino-Witten models by Wakimoto modules and uses the representation theory of \(SL(N)\) to reduce arbitrary three point functions to generalized Dotsenko-Fateev integrals. For this, the author describes the finite dimensional irreducible holomorphic representations of \(SL(N)\) and derives Wakimoto modules from the flag manifold construction for \(\widehat {sl} (N)\) Kac-Moody algebras. The intertwining operators that characterize the invariant subspaces and quotient spaces are expressed in terms of the screening currents, two- and three-point functions of primary fields are also studied and finally the generalized Dotsenko-Fateev integrals are reduced from Fock space matrix elements of an arbitrary three point function.