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.
https://hal-cea.archives-ouvertes.fr/cea-01509870
Contributeur : Emmanuelle De Laborderie
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Soumis le : mardi 18 avril 2017 - 16:10:33
Dernière modification le : mardi 24 avril 2018 - 17:20:13
Document(s) archivé(s) le : mercredi 19 juillet 2017 - 15:24:12
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〉
