## The Virasoro minimal string

Scott Collier, Lorenz Eberhardt, Beatrix Muehlmann, Victor A. Rodriguez

SciPost Phys. 16, 057 (2024) · published 26 February 2024

- doi: 10.21468/SciPostPhys.16.2.057
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### Abstract

We introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral. The worldsheet theory consists of Liouville CFT with central charge c$≥$ 25 coupled to timelike Liouville CFT with central charge 26-c. The double-scaled matrix integral has as its leading density of states the universal Cardy density of primaries in a two-dimensional CFT, thus motivating the name Virasoro minimal string. The duality holds for any value of the continuous parameter $c$ and reduces to the JT gravity/matrix integral duality in the large central charge limit. It thus provides a precise stringy realization of JT gravity. The main observables of the Virasoro minimal string are quantum analogues of the Weil-Petersson volumes, which are computed as absolutely convergent integrals of worldsheet CFT correlators over the moduli space of Riemann surfaces. By exploiting a relation of the Virasoro minimal string to three-dimensional gravity and intersection theory on the moduli space of Riemann surfaces, we are able to give a direct derivation of the duality. We provide many checks, such as explicit numerical - and in special cases, analytic - integration of string diagrams, the identification of the CFT boundary conditions with asymptotic boundaries of the two-dimensional spacetime, and the matching between the leading non-perturbative corrections of the worldsheet theory and the matrix integral. As a byproduct, we discover natural conformal boundary conditions for timelike Liouville CFT.

##### This publication has been updated

- Correction: The Virasoro minimal string on 2024-02-27

### Cited by 6

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Scott Collier, -
^{3}Lorenz Eberhardt, -
^{4}Beatrix Muehlmann, -
^{1}Victor A. Rodriguez

^{1}Princeton University^{2}Massachusetts Institute of Technology [MIT]^{3}Institute for Advanced Study, Princeton [IAS]^{4}McGill University