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.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP(3).

Automated summary

This article investigates the two-dimensional four-derivative conformal theory derived from the Nambu-Goto string by path-integration. By using the method of singular products, the author demonstrates that the one-loop approximation provides an exact solution. The solution can be conveniently described using minimal models, where the central charge c in the Kac spectrum depends on the parameters of the four-derivative action. This relation is nonlinear, allowing the mapping of the domain of physical parameters to c < 1, bypassing the KPZ barrier of the Liouville action.