Sphere and disk partition functions in Liouville and in matrix integrals

TL;DR

This paper compares sphere and disk partition functions in semiclassical Liouville theory and matrix integrals, finding exact matches and revealing that the JT gravity sphere partition function diverges.

Contribution

It provides a precise numerical comparison between Liouville and matrix integral partition functions, and demonstrates the divergence of the JT gravity sphere partition function.

Findings

Exact match between Liouville and matrix integral results for sphere/disk^2

The sphere partition function in JT gravity is infinite

Clarifies the relationship between Liouville theory and matrix models

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.