Stochastic Loewner evolution for conformal field theories with Lie-group symmetries

Bettelheim, E.; Gruzberg, I. A.; Ludwig, A. W. W.; Wiegmann, P.

Stochastic Loewner evolution for conformal field theories with Lie-group symmetries

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Description

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.