Non-critical string, Liouville theory and geometric bootstrap hypothesis

TL;DR

This paper investigates the limitations of existing Liouville theories in describing non-critical string dynamics, introduces a new geometric approach, and discusses the emergence of cut singularities in string amplitudes.

Contribution

It proposes a novel geometric bootstrap framework for Liouville theory, addressing issues with singularities in string amplitude calculations.

Findings

DOZZ solution leads to cut singularities in amplitudes

New geometric approach results in similar singularities

Formulation of a geometric bootstrap equation

Abstract

The applications of the existing Liouville theories for the description of the longitudinal dynamics of non-critical Nambu-Goto string are analyzed. We show that the recently developed DOZZ solution to the Liouville theory leads to the cut singularities in tree string amplitudes. We propose a new version of the Polyakov geometric approach to Liouville theory and formulate its basic consistency condition - the geometric bootstrap equation. Also in this approach the tree amplitudes develop cut singularieties.