On the Three-point Function in Minimal Liouville Gravity

TL;DR

This paper revisits and rederives structure constants in minimal models of conformal field theory, presenting them in a form useful for Liouville gravity, and provides explicit three- and two-point correlation numbers on the sphere.

Contribution

It offers a new derivation and reformulation of structure constants in minimal models tailored for Liouville gravity applications.

Findings

Rederived known structure constants in a new useful form.

Established analytic relations between minimal model constants and Liouville field theory.

Presented explicit three- and two-point correlation numbers on the sphere.

Abstract

The problem of the structure constants of the operator product expansions in the minimal models of conformal field theory is revisited. We rederive these previously known constants and present them in the form particularly useful in the Liouville gravity applications. Analytic relation between our expression and the structure constant in Liouville field theory is discussed. Finally we present in general form the three- and two-point correlation numbers on the sphere in the minimal Liouville gravity.