The complex Liouville string: The worldsheet
Scott Collier, Lorenz Eberhardt, Beatrix Mühlmann, Victor A. Rodriguez
SciPost Phys. 19, 033 (2025) · published 12 August 2025
- doi: 10.21468/SciPostPhys.19.2.033
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Abstract
We introduce a new two-dimensional string theory defined by coupling two copies of Liouville CFT with complex central charge $c=13± i \lambda$ 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.
Cited by 4
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Scott Collier,
- 2 Lorenz Eberhardt,
- 3 4 Beatrix Mühlmann,
- 5 6 Victor A. Rodriguez
- 1 Massachusetts Institute of Technology [MIT]
- 2 Institute for Theoretical Physics Amsterdam [ITFA]
- 3 Institute for Advanced Study [IAS]
- 4 McGill University
- 5 Princeton University
- 6 University of California, Santa Barbara [UCSB]