Journal of High Energy Physics (Sep 2021)

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

  • Dionysios Anninos,
  • Teresa Bautista,
  • Beatrix Mühlmann

Journal volume & issue
Vol. 2021, no. 9
pp. 1 – 30


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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.