The complex Liouville string: the worldsheet

TL;DR

This paper introduces a novel two-dimensional string theory with complex central charge, providing a consistent model of quantum gravity and deriving exact constraints on string amplitudes without explicit moduli space integrations.

Contribution

It presents the first consistent complex Liouville string model, deriving amplitude constraints analytically and setting the stage for further holographic and non-perturbative studies.

Findings

Derived constraints on string amplitudes from worldsheet theory

Solved specific examples like sphere four-point and torus one-point amplitudes

Established a foundation for holographic duality and non-perturbative analysis

Abstract

We introduce a new two-dimensional string theory defined by coupling two copies of Liouville CFT with complex central charge $c=13\pm i \lambda$ on the worldsheet. This string theory defines a novel, consistent and controllable model of two-dimensional quantum gravity. We use the exact solution of the worldsheet theory to derive stringent constraints on the analytic structure of the string amplitudes as a function of the vertex operator momenta. Together with other worldsheet constraints, this allows us to completely pin down the string amplitudes without explicitly computing the moduli space integrals. We focus on the case of the sphere four-point amplitude and torus one-point amplitude as worked examples. This is the first in a series of papers on the complex Liouville string: three subsequent papers will elucidate the holographic duality with a two-matrix integral, discuss worldsheet boundaries and non-perturbative effects, and connect the theory to de Sitter quantum gravity.