Liouville Quantum Gravity on the Riemann sphere
Probability
2015-06-08 v4 Mathematical Physics
math.MP
Abstract
In this paper, we rigorously construct 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-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly (Polyakov-Ray-Singer) formula for Liouville Quantum Gravity.
Cite
@article{arxiv.1410.7318,
title = {Liouville Quantum Gravity on the Riemann sphere},
author = {François David and Antti Kupiainen and Rémi Rhodes and Vincent Vargas},
journal= {arXiv preprint arXiv:1410.7318},
year = {2015}
}
Comments
Added conjectures relating Liouville quantum field theory to random planar map and optimal conditions in order to ensure existence of the unit volume Liouville measure