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The two-sphere partition function in two-dimensional quantum gravity
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DOI：10.1007/JHEP09(2021)116.png)
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Abstract
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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.
Keywords:
2D Gravity
Models of Quantum Gravity
Journal
IF:
5.5
Papers:
3.9W
Citations:
13.7W