Abstract
In this paper, we rigorously construct Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov. We establish some of its fundamental properties like conformal covariance under PSL\({_2(\mathbb{C})}\)-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly formula. We also make precise conjectures about the relationship of the theory to scaling limits of random planar maps conformally embedded onto the sphere.
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Communicated by F. Toninelli
A. Kupiainen: Supported by the Academy of Finland.
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David, F., Kupiainen, A., Rhodes, R. et al. Liouville Quantum Gravity on the Riemann Sphere. Commun. Math. Phys. 342, 869–907 (2016). https://doi.org/10.1007/s00220-016-2572-4
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DOI: https://doi.org/10.1007/s00220-016-2572-4