Abstract

We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ’s minimal models of 2D CFT as described by Felder & Silvotti and Dotsenko & Fateev (the “Coulomb gas formalism”). This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is symmetric (as in the Selberg integral itself) or, more generally, what we call “DF-symmetric,” we show that a number of apparent singularities are removable, as required for the construction of the minimal models via these methods.

中文翻译：

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类 Selberg 和 Dotsenko-Fateev 积分的奇异性

摘要

我们讨论基于 Selberg 积分建模的某些超几何积分的亚纯延拓，包括 Felder & Silvotti 和 Dotsenko & Fateev 所描述的 BPZ 二维 CFT 最小模型的 3 点和 4 点函数（“库仑气体形式主义”） 。这是通过被积函数奇点的几何分析来完成的。在被积函数对称的情况下（如塞尔伯格积分本身），或者更一般地说，我们称之为“DF 对称”，我们表明，根据构造最小模型的要求，许多明显的奇点是可去除的通过这些方法。