The singularities of Selberg- and Dotsenko-Fateev-like integrals

TL;DR

This paper analyzes the singularities of hypergeometric integrals related to Selberg and Dotsenko-Fateev models, providing a geometric approach to their meromorphic continuation and clarifying the nature of their singularities.

Contribution

It introduces a geometric method to study the singularities of Selberg- and Dotsenko-Fateev-like integrals, showing how certain apparent singularities are removable in symmetric cases.

Findings

Identifies conditions under which singularities are removable.

Provides a geometric framework for meromorphic continuation.

Clarifies the structure of integrals in 2D CFT models.

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 and Silvotti and Dotsenko and 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.