Liouville Quantum Gravity on the unit disk

Yichao Huang (1) , Rémi Rhodes (2) , Vincent Vargas (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work by Polyakov. In this paper, we investigate the case of simply connected domains with boundary. We also make precise conjectures about the relationship of this theory to scaling limits of random planar maps with boundary conformally embedded onto the disk.

Mots clés: Liouville Quantum Gravity; quantum field theory; Gaussian multiplica-tive chaos; KPZ formula; KPZ scaling laws; Polyakov formula; conformal anomaly

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]

Yichao Huang, Rémi Rhodes, Vincent Vargas. Liouville Quantum Gravity on the unit disk. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2018, ⟨10.1214/17-AIHP852⟩. ⟨hal-01161631⟩