Gauge symmetries and holographic anomalies of Chern-Simons and transgression AdS gravity

We review the issue of gauge and gravitational anomalies with backgrounds, offering a new outlook on some aspects of these questions. We compute the holographic anomalies of hypothetical theories dual, in the sense of the AdS-CFT correspondence, to Chern-Simons AdS gravity. Those anomalies are either gauge anomalies, associated to the AdS gauge group of the theory, or diffeomorphism anomalies, with each kind related to the other. AdS gauge anomalies include Weyl, Lorentz (gravitational) and gauge translations while diffeomorphism anomalies include gravitational and Weyl (or scale) anomalies. Our results therefore go beyond previous investigations on Chern-Simons AdS gravity holograpic anomalies, that dealt only with Weyl anomalies. Furthermore, our calculations were done allowing a non vanishing torsion, unlike previous works that considered only the zero torsion, or metric, case. As a result of using suitable action principles for Chern-Simons AdS gravity, coming from Transgression forms, we obtain finite results without the need for further regularization. Our results are of potential interest for Lovelock gravity theories, as it has been shown that the boundary terms dictated by the transgressions for Chern-Simons gravity are also suitable to regularize Lovelock theories. The Wess-Zumino consistency condition ensures that anomalies of the generic form computed here should appear for these and other theories.