Abstract
We review the issue of gauge and gravitational anomalies with backgrounds, maybe 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 gravities. 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. As a result of using suitable action principles por Chern-Simons AdS gravities, 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 gravities 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.
Highlights
Chern-Simons (CS) gravity have been investigated by many researchers during the last few decades, uncovering a wealth of interesting properties in many aspects of these theories
It has the disadvantage that the Noether charge associated to the gauge invariance vanishes in this case
Option II is more general, containing all the gauge transformations allowed by option
Summary
Chern-Simons (CS) gravity have been investigated by many researchers during the last few decades, uncovering a wealth of interesting properties in many aspects of these theories (see for instance [1,2,3,4,5,6]). The conformal anomaly induced by Chern-Simons gravitational theories was computed in [32] for 5D and 3D CS gravity (inducing Weyl anomalies in 4D and 2D CFTs respectively) and the generic form for arbitrary dimension was conjectured. This calculation was done only on the gravitational side, as the dual CFT theories are not known, but the result of doing this gravitational computation using several different methods was the same, and it was in agreement with what was to be expected from refs.
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