Stochastic Loewner evolution for conformal field theories with Lie-group   symmetries
  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. 
E. Bettelheim, I. A. Gruzberg, A. W. W. Ludwig, P. Wiegmann