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

TL;DR

This paper develops a group theoretical framework for Schramm--Loewner evolution processes linked to Wess--Zumino--Witten theories, enabling the construction of stochastic equations for more complex null vectors than previously considered.

Contribution

It introduces a novel group theoretical approach to connect Schramm--Loewner evolution with Wess--Zumino--Witten models, expanding the class of null vectors and associated growth processes.

Findings

Constructed stochastic differential equations for generalized null vectors.

Provided examples for null vectors of conformal weight 4 in affine Lie algebra representations.

Extended the connection between SLE processes and conformal field theories.

Abstract

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 $\widehat{\mathfrak{sl}}_{2}$ and $\widehat{\mathfrak{sl}}_{3}$.