The quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of $AdS_{4}$

TL;DR

The paper analyzes the quantum one-loop two-point function of higher-spin conformal currents in AdS$_4$ generated from a conformally coupled scalar. By constructing a gauge-invariant renormalization of the leading short-distance singularity, the authors find that the traceless Ward identities are violated at the quantum level, signaling a higher-spin trace anomaly, while current conservation persists. The singular part of the one-loop effective action for the external higher-spin field is derived; in the spin-2 case this reduces to a linearized Weyl-tensor-squared term, illustrating a concrete bulk manifestation of trace anomalies. The work provides a detailed RG framework for higher-spin gauge fields in AdS and strengthens the link between bulk HS dynamics and the boundary CFT under AdS/CFT, with implications for bulk mass generation and quantum consistency of HS interactions.

Abstract

An analysis of the structure and singularities of the one loop two point function of the higher spin traceless and conserved currents constructed from the single scalar field in $AdS$ space is presented. The detailed renormalization procedure is constructed and the quantum violation of the traceless Ward identity is investigated. The connection with the one loop effective action for higher spin gauge fields is discussed.