The two-sphere partition function in two-dimensional quantum gravity

• Main Authors: Dionysios Anninos, Teresa Bautista, Beatrix Mühlmann
• Format: Article
• Language: English
• Published: SpringerOpen 2021-09-01
• Series: Journal of High Energy Physics
• Subjects: 2D Gravity; Models of Quantum Gravity
• Online Access: https://doi.org/10.1007/JHEP09(2021)116

Abstract We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a round two-sphere saddle. We work in the Weyl gauge whereby the computation reduces to that for a (timelike) Liouville theory. We present results up to two-loops, including a discussion of contributions stemming from the gauge fixing procedure. We exhibit cancelations of ultraviolet divergences and provide a path integral computation of the central charge for timelike Liouville theory. Combining our analysis with insights from the DOZZ formula we are led to a proposal for an all orders result for the two-dimensional gravitational partition function on the two-sphere.