The Dilaton Wess-Zumino Action in 6 Dimensions from Weyl Gauging: Local Anomalies and Trace Relations

We extend a previous analysis on the derivation of the dilaton Wess-Zumino (WZ) action in $d=4$, based on the method of Weyl gauging, to $6$ dimensions. As in the previous case, we discuss the structure of the same action in dimensional regularization using 6-dimensional Weyl invariants, extracting the dilaton interactions in the most general scheme, with the inclusion of the local anomaly terms. As an application, we present the WZ action for the (2,0) tensor multiplet, which has been investigated in the past in the context of the $AdS_7/CFT_6$ holographic anomaly matching. We then extend to $d=6$ the investigation of fully traced correlation functions of EMT's, formerly presented in $d=4$, showing that their hierarchy is functionally related only to the first 6 correlators. We give the explicit expressions of these in the most general scheme, up to rank-4.