# Sugawara construction The Sugawara construction is a procedure used to build the energy-momentum tensor in the presence of the Kac-Moody algebra in the context of CFTs. It can be used to show, for example, that the energy-momentum tensor of the [[0601 Weiss-Zumino-Witten models|WZW]] model satisfies the [[0032 Virasoro algebra|Virasoro algebra]] and is therefore conformal. ## Refs - original: [[1968#Sugawara]] - [[0010 Celestial holography|celestial CFT]]: [[2020#Fan, Fotopoulos, Stieberger, Taylor]]