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arXiv · 2106.04532

The two-sphere partition function in two-dimensional quantum gravity at fixed area

Beatrix Mühlmann
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Abstract

We discuss two-dimensional quantum gravity coupled to conformal matter and fixed area in a semiclassical large and negative matter central charge limit. In this setup the gravity theory -- otherwise highly fluctuating -- admits a round two-sphere saddle. We discuss the two-sphere partition function up to two-loop order from the path integral perspective. This amounts to studying Feynman diagrams incorporating the fixed area constraint on the round two-sphere. In particular we find that all ultraviolet divergences cancel to this order. We compare our results with the two-sphere partition function obtained from the DOZZ formula.

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Beatrix Mühlmann. 2021-06-08. The two-sphere partition function in two-dimensional quantum gravity at fixed area. https://doi.org/10.1007/jhep09(2021)189

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