Schramm--Loewner-evolution-type growth processes corresponding to Wess--Zumino--Witten theories

A group theoretical formulation of Schramm–Loewner-evolution-type growth processes corresponding to Wess–Zumino–Witten theories is developed that makes it possible to construct stochastic differential equations associated with more general null vectors than the ones considered in the most fundamental example in [Alekseev et al., Lett. Math. Phys. 97, 243-261 (2011)]. Also given are examples of Schramm–Loewner-evolution-type growth processes associated with null vectors of conformal weight $4$ in the basic representations of ${\widehat{\mathfrak{s}\mathfrak{l}}}_2$ and ${\widehat{\mathfrak{s}\mathfrak{l}}}_3$.