The Virasoro Minimal String

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 $c\ge 25$ 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.

14 pages of summary and results, 113 pages in total, ancillary mathematica notebook

References in corpus (20)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models
• Bootstrap in Supersymmetric Liouville Field Theory. I. NS Sector
• Little String Amplitudes (and the Unreasonable Effectiveness of 6D SYM)
• Notes on Liouville Theory at c<=1
• Multi-instantons in minimal string theory and in matrix integrals
• FZZT branes in JT gravity and topological gravity
• dS${}_2$ Supergravity
• Black hole microstate counting from the gravitational path integral
• Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes
• Revisiting the Logarithmic Corrections to the Black Hole Entropy
• D-instanton Effects in Type IIB String Theory
• Five-point correlation numbers in minimal Liouville gravity and matrix models
• Off-shell Partition Functions in 3d Gravity
• Approximate CFTs and Random Tensor Models
• A convergent genus expansion for the plateau
• 2D dilaton gravity and the Weil-Petersson volumes with conical defects
• Constructing all BPS black hole microstates from the gravitational path integral
• Euclidean wormholes for individual 2d CFTs

Cited by in corpus (33)

• 3d gravity from Virasoro TQFT: Holography, wormholes and knots
• Multiboundary wormholes and OPE statistics
• A microscopic realization of dS${}_3$
• The dilaton gravity hologram of double-scaled SYK
• Wormholes, branes and finite matrices in sine dilaton gravity
• The complex Liouville string: the matrix integral
• The complex Liouville string: the worldsheet
• Supersymmetric Virasoro Minimal Strings
• 3d Gravity as a random ensemble
• TQFT gravity and ensemble holography
• A localising AdS${}_3$ sigma model
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Branes in JT (super)gravity from group theory
• The complex Liouville string: worldsheet boundaries and non-perturbative effects
• The complex Liouville string: the gravitational path integral
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• Les Houches lectures on two-dimensional gravity and holography
• Quantum group origins of edge states in double-scaled SYK
• Modular-invariant random matrix theory and AdS${}_3$ wormholes
• Non-Perturbative Corrections to Charged Black Hole Evaporation
• Gravitational wavefunctions in JT supergravity
• On the Virasoro fusion kernel at $c=25$
• On Krichever tau-function and Verlinde formula
• Open-closed 3d gravity as a random ensemble
• Discrete JT gravity as an Ising model
• $x-y$ swap for $(2,2p+1)$ minimal string
• JT de Sitter Gravity as a Model of Coleman-de Luccia Tunneling
• On construction of correlation numbers in super Minimal Liouville Gravity in the Ramond sector
• Les Houches lecture notes on moduli spaces of Riemann surfaces
• Probabilistic construction of non compactified imaginary Liouville field theory
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• A Renormalization Group Analysis of the Ising Model Coupled to Causal Dynamical Triangulations
• Asymptotics of Weil-Petersson volumes and two-dimensional quantum gravities