Nambu-Goto string as a higher-derivative Liouville theory

TL;DR

This paper introduces a higher-derivative generalization of the Liouville action to describe the Nambu-Goto string, revealing quantum effects and broader applicability compared to the traditional Liouville theory.

Contribution

It proposes a novel higher-derivative Liouville action that models the Nambu-Goto string and establishes an equivalence with a four-derivative action, extending the theoretical framework.

Findings

Nambu-Goto string can be described by a higher-derivative Liouville theory.

Quantum effects revive higher-derivative terms that are classically negligible.

Broader applicability of the model compared to standard Liouville theory.

Abstract

I propose a generalization of the Liouville action which corresponds to the Nambu-Goto string like the usual Liouville action corresponds to the Polyakov string. The two differ by higher-derivative terms which are negligible classically but revive quantumly. An equivalence with the four-derivative action suggests that the Nambu-Goto string in four dimensions can be described by the (4,3) minimal model analogously to the critical Ising model on a dynamical lattice. While critical indices are the same as in the usual Liouville theory, the domain of applicability becomes broader.