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arXiv · 2301.03750

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

Ethan Sussman
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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.

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Ethan Sussman. 2023-01-10. The singularities of Selberg- and Dotsenko-Fateev-like integrals. https://doi.org/10.1007/s00023-023-01402-1

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