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Our purpose is to pursue the rigorous construction of Liouville Quantum FieldTheory on Riemann surfaces initiated by F. David, A. Kupiainen and the last twoauthors in the context of the Riemann sphere and inspired by the 1981 seminalwork by Polyakov. In this paper, we investigate the case of simply connecteddomains with boundary. We also make precise conjectures about the relationshipof this theory to scaling limits of random planar maps with boundaryconformally embedded onto the disk.

Liouville Quantum Gravity on the unit disk