Stress-Energy in Liouville Conformal Field Theory

Abstract

We construct the Stress-Energy tensor correlation functions in probabilistic Liouville Conformal Field Theory (LCFT) on the two dimensional sphere S 2 by studying the variation of the LCFT correlation functions with respect to a smooth Riemannian metric on S 2 . In particular we derive Conformal Ward identities for these correlations. This forms the basis for the construction of a representation of the Virasoro algebra on the canonical Hilbert space of the LCFT.