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

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 Poincaré-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.

19 pages. V2: refs added, typos corrected. V3: to appear in JHEP

References in corpus (12)

• Effective action in a higher-spin background
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• Partition function of free conformal higher spin theory
• Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• On conformal higher spin wave operators
• Arbitrary spin conformal fields in (A)dS
• $C_T$ for conformal higher spin fields from partition function on conically deformed sphere
• Determinants and conformal anomalies of GJMS operators on spheres
• Holographic formula for the determinant of the scattering operator in thermal AdS
• Holography beyond conformal invariance and AdS isometry?