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arXiv · 2106.01665

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

Dionysios Anninos·Teresa Bautista·Beatrix Mühlmann
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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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Dionysios Anninos, Teresa Bautista, Beatrix Mühlmann. 2021-06-03. The two-sphere partition function in two-dimensional quantum gravity. https://doi.org/10.1007/jhep09(2021)116

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