Gauge Symmetries and Holographic Anomalies of Chern-Simons and Transgression AdS Gravity

TL;DR

This paper investigates gauge and gravitational anomalies in Chern-Simons and Transgression AdS gravities, computing holographic anomalies in dual theories and showing how suitable action principles yield finite results without extra regularization.

Contribution

It introduces a method to compute holographic anomalies using Transgression forms, providing finite results and insights applicable to Lovelock gravity theories.

Findings

Finite holographic anomalies obtained without additional regularization.

Anomalies related to AdS gauge groups and diffeomorphisms are interconnected.

Boundary terms from Transgression forms regularize Lovelock theories.

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.