Liouville Quantum Gravity on the Riemann sphere
  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. 
Fran\c{c}ois David, Antti Kupiainen, R\'emi Rhodes, Vincent Vargas
math.PR math-ph math.MP