Two and three-point functions in Liouville theory

TL;DR

This paper constructs two- and three-point correlation functions in Liouville theory with generic coefficients, proving the Liouville equation of motion at the three-point level and discussing implications for string theory.

Contribution

It generalizes the Goulian-Li continuation to arbitrary real coefficients and verifies the Liouville equation of motion for three-point functions, advancing the understanding of Liouville correlators.

Findings

Constructed explicit two- and three-point functions for Liouville exponentials.

Proved the Liouville equation of motion at the three-point correlation level.

Discussed implications for noncritical string theory and the structure of Liouville correlators.

Abstract

Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument in favour of the procedure we prove the Liouville equation of motion on the level of three-point functions. The analytical structure of the correlation functions as well as some of its consequences for string theory are discussed. This includes a conjecture on the mass shell condition for excitations of noncritical strings. We also make a comment concerning the correlation functions of the Liouville field itself.