Conformal Ward and BPZ Identities for Liouville quantum field theory

Antti Kupiainen, Rémi Rhodes, Vincent Vargas

Published 2015-12-06Version 1

In this work, we continue the constructive probabilistic approach to the Liouville Quantum Field theory (LQFT) started in \cite{DKRV}. We give a rigorous construction of the stress energy tensor in LQFT and prove the validity of the conformal Ward identities. Within this framework, we also derive the Belavin-Polyakov-Zamolodchikov (BPZ) differential equations of order 2 for the associated degenerate fields of the theory. As an application, we give an explicit formula for the 4 point correlation function with a degenerate field insertion leading to a proof of a non trivial functional relation on the 3 point structure constant derived earlier by Teschner.