Bulk correlation functions in 2D quantum gravity

TL;DR

This paper calculates bulk 3- and 4-point tachyon correlators in 2D Liouville gravity with non-rational matter central charge c<1, comparing continuous and discrete approaches, and deriving new structure constants.

Contribution

It introduces a general formula for matter 3-point OPE structure constants and compares two different methods for computing correlators in 2D quantum gravity.

Findings

Derived a general formula for matter 3-point OPE structure constants.

Compared continuous CFT and discrete formulations of 2D quantum gravity.

Analyzed correlators in both approaches to establish consistency.

Abstract

We compute bulk 3- and 4-point tachyon correlators in the 2d Liouville gravity with non-rational matter central charge c<1, following and comparing two approaches. The continuous CFT approach exploits the action on the tachyons of the ground ring generators deformed by Liouville and matter ``screening charges''. A by-product general formula for the matter 3-point OPE structure constants is derived. We also consider a ``diagonal'' CFT of 2D quantum gravity, in which the degenerate fields are restricted to the diagonal of the semi-infinite Kac table. The discrete formulation of the theory is a generalization of the ADE string theories, in which the target space is the semi-infinite chain of points.