Sphere and disk partition functions in Liouville and in matrix integrals

Abstract

We compute the sphere and disk partition functions in semiclassical Liouville and analogous quantities in double-scaled matrix integrals. The quantity sphere/disk^2 is unambiguous and we find a precise numerical match between the Liouville answer and the matrix integral answer. An application is to show that the sphere partition function in JT gravity is infinite.

27 pages

References in corpus (6)

• An Investigation of AdS${}_2$ Backreaction and Holography
• JT gravity as a matrix integral
• Dilaton-gravity, deformations of the minimal string, and matrix models
• The Disk Partition Function in String Theory
• The two-sphere partition function in two-dimensional quantum gravity at fixed area
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• JT Gravity in de Sitter Space and the Problem of Time
• dS${}_2$ Supergravity
• On-Shell Action for Type IIB Supergravity and Superstrings on $Ad{S}_5\times S^5$
• The Torus One-Point Diagram in Two-Dimensional String Cosmology
• Holographic Weyl anomaly in string theory
• Boundary terms in string field theory
• The complex Liouville string: the gravitational path integral
• Finite cut-off JT and Liouville quantum gravities on the disk at one loop
• The semiclassical gravitational path integral and random matrices
• The Fate of Nucleated Black Holes in de Sitter Quantum Gravity