A systematic construction of super W-algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by Hamiltonian reduction. A classification, according to the conformal spin defined by an improved energymomentum tensor, is discussed in general terms for all super L...

This is a review of recent work on the chiral extensions of the WZNW phase space describing both the extensions based on fields with generic monodromy as well as those using Bloch waves with diagonal monodromy. The symplectic form on the extended phase space is inverted in both cases and the chiral WZNW fields are found to satisfy quadratic Poisson bracket relations characterized by monodromy d...

We derive a generalization of the classical dynamical Yang-Baxter equation (CDYBE) on a self-dual Lie algebra G by replacing the cotangent bundle T G in a geometric interpretation of this equation by its Poisson-Lie (PL) analogue associated with a factorizable constant r-matrix on G. The resulting PL-CDYBE, with variables in the Lie group G equipped with the Semenov-Tian-Shansky Poisson bracket...

In a series of papers [1] we have presented a new approach to the old problem of the covariant quantization of the superstring. The fields of the classical superstring are x(z, z̄) and two (i=1,2) spacetime spinors θ(z, z̄) where m = 0, . . . , 9 is a vector index and α = 1, . . . , 16 the index of a real chiral spinor. A natural choice as action might seem to be the supersymmetric line element S...

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 cer...

We study perturbatively the (conformal) WZNW model. At one loop we compute one-particle irreducible twoand three-point current correlation functions, both in the conventional version and in the classically equivalent, chiral, nonlocal, induced version of the model. At two loops we compute the two-point function and find that it vanishes (modulo infrared-induced logarithms). We use dimensional r...