Liouville Quantum Gravity on the Riemann sphere

Abstract : In this paper, we rigorously construct 2d Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov Quantum Geometry of bosonic strings. We also establish some of its fundamental properties like conformal covariance un-der P SL 2 (C)-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly (Polyakov-Ray-Singer) formula for Liouville Quantum Gravity.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01081085
Contributor : Rémi Rhodes <>
Submitted on : Thursday, November 6, 2014 - 9:27:54 PM
Last modification on : Friday, October 4, 2019 - 1:35:52 AM
Long-term archiving on : Saturday, February 7, 2015 - 11:27:02 AM

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  • HAL Id : hal-01081085, version 1

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François David, Antti Kupiainen, Rémi Rhodes, Vincent Vargas. Liouville Quantum Gravity on the Riemann sphere. Communications in Mathematical Physics, Springer Verlag, 2016, 342 (3), pp.869-907. ⟨hal-01081085⟩

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