The complex Liouville string: the matrix integral

TL;DR

This paper establishes a duality between the complex Liouville string, defined by coupling two Liouville theories with complex central charges, and a two-matrix integral characterized by its spectral curve, enabling recursive amplitude computations.

Contribution

It introduces a duality between the complex Liouville string and a two-matrix integral, providing a new controllable example of holographic duality with detailed analytic structure analysis.

Findings

The duality is explicitly constructed and tested.

Perturbative string amplitudes are computed via topological recursion.

The spectral curve encodes the string theory's analytic properties.

Abstract

We propose a duality between the complex Liouville string and a two-matrix integral. The complex Liouville string is defined by coupling two Liouville theories with complex central charges $c = 13 \pm i \lambda$ on the worldsheet. The matrix integral is characterized by its spectral curve which allows us to compute the perturbative string amplitudes recursively via topological recursion. This duality constitutes a controllable instance of holographic duality. The leverage on the theory is provided by the rich analytic structure of the string amplitudes that we discussed in arXiv:2409.18759 and allows us to perform numerous tests on the duality.