Fuchsian systems for Dotsenko-Fateev multipoint correlation functions and similar integrals of hypergeometric type

TL;DR

This paper extends the analysis of Dotsenko-Fateev integrals, showing they satisfy Fuchsian systems of differential equations, which helps in understanding their local behavior near singularities in conformal field theory.

Contribution

It introduces generalized Fuchsian systems for multipoint Dotsenko-Fateev integrals, broadening the scope of their analytical and local expansion properties.

Findings

Constructed Fuchsian systems for multipoint correlators

Provided local solution expansions near singularities

Extended the third-order ODE framework to PDE systems

Abstract

The Dotsenko-Fateev integral is an analytic function of one complex variable expressing the amplitude in the 4-point correlator of the 2D conformal field theory. Dotsenko-Fateev found ODE of third order with Fuchsian singularities satisfied by their integral. In the present paper, this work is extended to generalized Dotsenko-Fateev integrals, in particular those associated to arbitrary multipoint correlators, and Pfaff systems of PDE of Fuchsian type are constructed for them. The ubiquity of the Fuchsian systems is in that they permit to obtain local expansions of solutions in the neighborhoods of singularities of the system.