The singularities of Selberg-- and Dotsenko--Fateev-like integrals
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- 10.48550/arXiv.2301.03750
- arXiv:
- arXiv:2301.03750
- Bibcode:
- 2023arXiv230103750S
- Keywords:
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- Mathematical Physics;
- Mathematics - Classical Analysis and ODEs;
- Primary 32A20;
- Secondary 33C60;
- 33C90;
- 81T40
- E-Print:
- 56 pages