Obstruction tensors in Weyl geometry and holographic Weyl anomaly

Recently a generalization of the Fefferman-Graham gauge for asymptotically locally AdS spacetimes, called Weyl-Fefferman-Graham (WFG) gauge, has been proposed. It was shown that WFG induces Weyl geometry on conformal boundary. The consists metric and connection. Thus, this is useful setting studying dual field theories with background symmetry. Working in formalism, we find obstruction tensors, which are Weyl-covariant tensors appear as poles expansion bulk even boundary dimensions. We see these Weyl-obstruction can be used building blocks anomaly theory. then compute $6d$ $8d$ contribution from structure appears cohomologically trivial modifications. Expressed terms Weyl-Schouten tensor extended results holographic up to also reveal hints its expression any dimension.