Single-channel correlators and residue calculus

TL;DR

This paper introduces a method using residue calculus to compute single-channel correlation functions in conformal theories, providing explicit examples and a general formula for structure constants.

Contribution

It presents a novel application of residue calculus to compute single-channel correlators and derives a generic formula for their structure constants in conformal models.

Findings

Explicit computation of correlation functions using residue calculus.

Derivation of a general expression for structure constants.

Application to minimal models and parafermionic theories.

Abstract

Some simple (namely, single-channel) correlation functions involving an arbitrary number of fields are computed by means of a direct application of the residue calculus, through partial fraction expansions. Examples are presented in minimal models and parafermionic conformal theories. A generic factorized expression is deduced for the corresponding single-channel structure constants.