Holographic $SO(2,d)$ anomaly

TL;DR

This paper explores the holographic $SO(2,d)$ anomaly within AdS gravity, systematically constructing the anomaly structure, characteristic class, and boundary effective action, highlighting the role of the ruler field.

Contribution

It establishes the descendent structure of the holographic $SO(2,d)$ anomaly and explicitly constructs covariant and consistent currents using the ruler field.

Findings

Constructed the anomaly characteristic class and bulk Chern-Simons like action.

Presented the anomalous conservation law in covariant and consistent forms.

Explicitly constructed covariant and consistent currents with the ruler field.

Abstract

In the $SO(2,d)$ gauge theory formalism of AdS gravity established in arXiv:1811.05286, the dynamics of bulk gravity emerges from the vanishing of the boundary covariant anomaly for the $SO(2,d)$ conservation law. In parallel with the known results on chiral anomalies, we establish the descendent structure of the holographic $SO(2,d)$ anomaly. The corresponding anomaly characteristic class, bulk Chern-Simons like action as well as the boundary effective action are constructed systematically. The anomalous conservation law is presented both in the covariant and consistent formalisms. Due to the existence of the ruler field, not only the Bardeen-Zumino polynomial, but also the covariant and consistent currents are explicitly constructed.