Generalized Coulomb-gas formalism for two dimensional critical models based on SU(2) coset construction

Conformal theories associated with the coset construction SU(2)k x SU(2)l/SU(2)k+l are described by a generalized Coulomb-gas formalism. An integrable lattice model obtained by k fusions of the 6-vertex model has a continuous critical line containing the level-k Wess-Zumino-Witten model. Its continuum limit is described by tensor products of the parafermionic and free bosonic sectors. Modification of its boundary conditions by the introduction of floating charges, yields the coset models. The discussion extends to non-unitary models. Special attention is paid to the case k=2, corresponding to N=1 supersymmetry. (orig.)