Exact solution of higher-derivative conformal theory and minimal models

TL;DR

This paper provides an exact solution to a specific two-dimensional four-derivative conformal theory derived from the Nambu-Goto string, revealing a nonlinear relation between parameters and the minimal models with central charge less than one.

Contribution

It introduces an exact one-loop solution for the four-derivative conformal theory, connecting it to minimal models and bypassing the KPZ barrier.

Findings

Exact one-loop solution derived

Central charge c<1 mapped from parameters

Bypasses KPZ barrier in Liouville theory

Abstract

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.