We introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

中文翻译：

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关于手性CFT中多组分区的模算子

我们引入了一种新方法，可以在一般手性保形场理论中为多组分区域找到富田-竹崎模块化流。我们的方法基于主场的局部性和分析性以及所谓的Kubo-Martin-Schwinger（KMS）条件。这些特征可以用来将问题转化为沿区域切割的复杂平面的覆盖上的Riemann-Hilbert问题，这等效于模块化哈密顿量矩阵元素的积分方程。考虑实例。