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Liouville Quantum Gravity on the Riemann sphere

François David 1 Antti Kupiainen 2 Rémi Rhodes 3 Vincent Vargas 4, 5
1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 Department of Mathematics and Statistics [Helsinki]
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
4 ENS Paris - École normale supérieure - Paris
5 DMA - Département de Mathématiques et Applications - ENS Paris
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 under PSL$_2(\mathbb{C})$-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly (Polyakov-Ray-Singer) formula for Liouville Quantum Gravity.
Keywords : KPZ formula Gaussian multiplicative chaos quantum field theory Polyakov formula KPZ scaling laws Liouville Quantum Gravity
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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, pp.869 - 907. ⟨10.1007/s00220-016-2572-4⟩. ⟨cea-01509870⟩

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