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Abstract In the SO (2, d ) gauge theory formalism of AdS gravity established in Wang and Song (2021 Class. Quantum Grav. 38 205002), 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.
Wang et al. (Mon,) studied this question.