On the Weyl anomaly of 4D Conformal Higher Spins: a holographic approach

TL;DR

This paper derives the full Weyl anomaly for 4D conformal higher spin fields using a holographic approach, connecting bulk one-loop effective actions with boundary anomalies, and confirms previous boundary results.

Contribution

It provides a holographic derivation of both type-A and type-B Weyl anomalies for 4D conformal higher spins, including new insights into their bulk-boundary correspondence.

Findings

Holographic computation matches boundary anomaly results

Type-A and type-B anomalies derived from bulk one-loop actions

Assumption of Lichnerowicz-type coupling facilitates anomaly calculation

Abstract

We present a first attempt to derive the full (type-A and type-B) Weyl anomaly of four dimensional conformal higher spin (CHS) fields in a holographic way. We obtain the type-A and type-B Weyl anomaly coefficients for the whole family of 4D CHS fields from the one-loop effective action for massless higher spin (MHS) Fronsdal fields evaluated on a 5D bulk Poincar\'e-Einstein metric with an Einstein metric on its conformal boundary. To gain access to the type-B anomaly coefficient we assume, for practical reasons, a Lichnerowicz-type coupling of the bulk Fronsdal fields with the bulk background Weyl tensor. Remarkably enough, our holographic findings under this simplifying assumption are certainly not unknown: they match the results previously found on the boundary counterpart under the assumption of factorization of the CHS higher-derivative kinetic operator into Laplacians of "partially massless" higher spins on Einstein backgrounds.