Liouville Conformal Field Theory on the higher-dimensional sphere

Baptiste Cerclé

Published 2019-12-19Version 1

Providing a rigorous definition to the two-dimensional Liouville Quantum Field Theory as introduced by Polyakov in his 1981 seminal work has been a challenging problem over the past few years. Recent developments in the study of conformal geometry in dimension higher than two has naturally led to a generalisation of Polyakov formalism to a higher-dimensional context. In this document we wish to provide a rigorous construction of Liouville Conformal Field Theory on the even-dimensional sphere, at both the classical and the quantum level; the properties of the objects thus defined are in agreement with the ones expected in the physics literature.