Exact solution of higher-derivative conformal theory and minimal models

I investigate the two-dimensional four-derivative conformal theory that emerges from the Nambu-Goto string after the path-integration over all fields but the metric tensor. Using the method of singular products which accounts for tremendous cancellations in perturbation theory, I show the (intelligent) one-loop approximation to give an exact solution. It is conveniently described through the minimal models where the central charge $c$ in the Kac spectrum depends on the parameters of the four-derivative action. The relation is nonlinear so the domain of physical parameters is mapped onto $c<1$ thus bypassing the KPZ barrier of the Liouville action.