  The Stochastic Loewner evolution is a recent tool in the study of
two-dimensional critical systems. We extend this approach to the case of
critical systems with continuous symmetries, such as SU(2) Wess-Zumino-Witten
models, where domain walls carry an additional spin 1/2 degree of freedom. We
show that the stochastic evolution results in the Knizhnik-Zamolodchikov
equation for correlation functions.
