We study the WZNW models based on nonstandard bilinear forms. We approach the problem from algebraic, perturbative and functional exact methods. It is shown that even in the case of integer k we can find irrational CFT’s. We prove that when the base group is noncompact with nonabelian maximal compact subgroup, the KacMoody representations are nonunitary.

Using a gauge invariant reduction we directly integrate the SL(2,R)/U(1) WZNW theory. We prove that the conserved parafermions of this theory are coset currents. Quantum mechanically, the parafermion algebra, the energy-momentum tensor, and ‘auxiliary’ parafermions are deformed in a self-consistent manner.

Working at the level of Poisson brackets, we describe the extension of the generalized Wakimoto realization of a simple Lie algebra valued current, J, to a corresponding realization of a group valued chiral primary field, b, that has diagonal monodromy and satisfies Kb ′ = Jb. The chiral WZNW field b is subject to a monodromy dependent exchange algebra, whose derivation is reviewed, too.

We study four point correlation functions of the spin 1 operators in the SU(2)0 WZNW model. The general solution which is everywhere single-valued has logarithmic terms and thus has a natural interpretation in terms of logarithmic conformal field theory. These are not invariant under all the crossing symmetries but can remain if fields possess additional quantum numbers. [email protected]...