Bulk correlation functions in 2d quantum gravity

We compute the bulk three- and four-point tachyon correlators in the 2d Liouville gravity with a nonrational matter central charge c < 1, using and comparing two approaches. The continuous CFT approach exploits the action on the tachyons of the ground-ring generators deformed with Liouville and matter screening charges. We derive a general formula for the matter three-point OPE structure constants as a by-product. 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.