TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.2.057
TI  - The Virasoro minimal string
PY  - 2024/02/26
UR  - https://scipost.org/SciPostPhys.16.2.057
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 2
SP  - 057
A1  - Collier, Scott
AU  - Eberhardt, Lorenz
AU  - Muehlmann, Beatrix
AU  - Rodriguez, Victor A.
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.16.2.057,
	title={{The Virasoro minimal string}},
	author={Scott Collier and Lorenz Eberhardt and Beatrix Muehlmann and Victor A. Rodriguez},
	journal={SciPost Phys.},
	volume={16},
	pages={057},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.2.057},
	url={https://scipost.org/10.21468/SciPostPhys.16.2.057},
}