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 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.

arXiv commentAdded conjectures relating Liouville quantum field theory to random planar map and optimal conditions in order to ensure existence of the unit volume Liouville measure

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Cited by in corpus (5)

• Lecture notes on Gaussian multiplicative chaos and Liouville Quantum Gravity
• Multiplicative chaos measures for a random model of the Riemann zeta function
• Interfaces in the vertex-decorated Ising model on random triangulations of the disk
• The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phase
• On the logarithm of the characteristic polynomial of the Ginibre ensemble