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.
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Anninos, D., Bautista, T. & Mühlmann, B. The two-sphere partition function in two-dimensional quantum gravity. J. High Energ. Phys. 2021, 116 (2021). https://doi.org/10.1007/JHEP09(2021)116
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DOI: https://doi.org/10.1007/JHEP09(2021)116