The complex Liouville string: The matrix integral
Scott Collier, Lorenz Eberhardt, Beatrix Mühlmann, Victor A. Rodriguez
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 ± i \lambda <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> <mml:mo>±</mml:mo> <mml:mi>i</mml:mi> <mml:mi>λ</mml:mi> </mml:mrow> </mml:math> 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.