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

    Source link


    Leave A Reply