Three-Point Function in Perturbed Liouville Gravity

TL;DR

This paper explicitly computes the three-point correlation function in perturbed Liouville gravity coupled with 2D quantum gravity using a free field approach, confirming its exactness and extending previous results.

Contribution

It introduces a free field method to compute three-point functions in perturbed Liouville gravity, including winding violating cases without spectral flow.

Findings

Confirmed the free field approach yields exact three-point functions.

Extended previous calculations to include winding violating functions.

Validated the representation for string theory in AdS_3 space.

Abstract

Three-point correlation function in perturbed conformal field theory coupled to two-dimensional quantum gravity (perturbed Liouville gravity) is explicitly computed by using the free field approach. The representation considered here is the one recently proposed in hep-th/0511252 to describe the string theory in AdS_3 space. Consequently, this computation extends previous results which presented free field calculations of particular cases of string amplitudes, and confirms that the free field approach leads to the exact result. Remarkably, this representation allows to compute winding violating three-point functions without making use of the spectral flow operator.