The complex Liouville string: the matrix integral

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 $c=13\pm i\hat{I}»$ 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.

52 pages + appendices