Schramm–Loewner evolution (SLE) is a random process that gives a useful description of fractal curves. After its introduction, many works concerning the connection between SLE and conformal field theory (CFT) have been carried out. In this paper, we develop a new method of coupling SLE with a Wess–Zumino–Witten (WZW) model for [Formula: see text], an example of CFT, relying on a coset construction of Virasoro minimal models. Generalizations of SLE that correspond to WZW models were proposed by previous works [E. Bettelheim et al., Stochastic Loewner evolution for conformal field theories with Lie group symmetries, Phys. Rev. Lett. 95 (2005) 251601] and [Alekseev et al., On SLE martingales in boundary WZW models, Lett. Math. Phys. 97 (2011) 243–261], in which the parameters in the generalized SLE for [Formula: see text] were related to the level of the corresponding [Formula: see text]-WZW model. The present work unveils the mechanism of how the parameters were chosen, and gives a simpler proof of the result in these previous works, shedding light on a new perspective of SLE/WZW coupling.

中文翻译：

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Virasoro 最小模型的陪集构造和 Wess-Zumino-Witten 理论与 Schramm-Loewner 演化的耦合

Schramm-Loewner 演化 (SLE) 是一个随机过程，它提供了对分形曲线的有用描述。在引入之后，已经开展了许多关于 SLE 与共形场论 (CFT) 之间联系的工作。在本文中，我们开发了一种将 SLE 与 Wess-Zumino-Witten (WZW) 模型耦合的新方法，该方法是 CFT 的一个示例，依赖于 Virasoro 最小模型的陪集构造。与 WZW 模型相对应的 SLE 的推广是由先前的工作 [E. Bettelheim 等人，具有李群对称性的共形场理论的随机 Loewner 演化，物理学。牧师莱特。95 (2005) 251601] 和 [Alekseev 等人，关于边界 WZW 模型中的 SLE 鞅，Lett。数学。物理。97 (2011) 243–261]，其中广义 SLE 中的参数为 [公式：见文]分别与对应的[公式：见文]-WZW模型的级别有关。目前的工作揭示了如何选择参数的机制，并为这些先前工作的结果提供了更简单的证明，揭示了 SLE/WZW 耦合的新视角。