Cerclé Baptiste
École Polytechnique Fédérale de Lausanne, MA A2 397, Station 8, 1015 Lausanne, Switzerland.
Commun Math Phys. 2025;406(6):147. doi: 10.1007/s00220-025-05328-z. Epub 2025 May 30.
In this document we prove higher equations of motion at the level 2 for boundary Liouville Conformal Field Theory. As a corollary we present a new derivation of the Belavin-Polyakov-Zamolodchikov differential equations. Our method of proof does not rely on the mating of trees machinery but rather exploits the symmetries of the model through the Ward identities it satisfies. To do so we provide a definition of derivatives of the correlation functions with respect to a boundary insertion which was lacking in the existing literature, and introduce a new notion of descendant fields related to these Ward identities.
在本文档中，我们证明了边界刘维尔共形场论二级水平下的高阶运动方程。作为推论，我们给出了Belavin-Polyakov-Zamolodchikov微分方程的一种新推导。我们的证明方法不依赖于树交配机制，而是通过模型满足的沃德恒等式来利用其对称性。为此，我们给出了现有文献中所缺乏的关于关联函数相对于边界插入的导数的定义，并引入了与这些沃德恒等式相关的后代场的新概念。
