Analytic continuation of 3-point functions of the conformal field theory

TL;DR

This paper demonstrates that 3-point functions in various conformal field theories, including minimal models and Liouville theory, can be derived through systematic analytical continuation from minimal model correlators.

Contribution

It introduces a unified method to obtain 3-point functions across different conformal field theories via analytical continuation from minimal models.

Findings

3-point functions of Liouville and minimal models are connected

Analytical continuation can generate continuous charge values

Unified approach simplifies calculations across models

Abstract

It is shown that the general 3-point function $<\Phi_{a} \Phi_{b} \Phi_{c}>$, with continuous values of charges $a, b, c$ of a statistical model operators, and the 3-point function of the Liouville model, could all be obtained by successive analytical continuations starting from the 3-point function of the minimal model.