Generalized Curvature and Ricci Tensors for a Higher Spin Potential and the Trace Anomaly in External Higher Spin Fields in AdS_{4} Space

TL;DR

This paper analyzes the curvature and Ricci tensors for higher spin fields in AdS4, deriving identities and showing how to eliminate the trace anomaly using curvature-based techniques in a conformal scalar context.

Contribution

It introduces a generalized curvature formalism for higher spin potentials and applies it to trace anomaly analysis in external higher spin fields in AdS4.

Findings

All Ricci tensors expressed as differential operators on the Fronsdal term

Weyl variations of Ricci tensor squares can eliminate the anomaly

Formalism simplifies higher spin curvature and anomaly calculations

Abstract

The curvature of a higher spin potential as constructed in a previous article of the same authors arXiv:0705.3528 is applied to the analysis of the linearized trace anomaly obtained from the quadratic part of the effective action for a conformally coupled scalar with linearized interaction with the external higher spin fields arXiv:hep-th/0602067. The spin is restricted to four to profit from technical simplifications but without reducing the problem in principle. The issue includes the calculation of all Ricci tensors as multiple traces of the curvature, the derivation of all primary and secondary Bianchi identities, expressing all Ricci tensors as differential operators applied to the Fronsdal term, calculating the Weyl variation of these, and showing finally that Weyl variations of integrals over contracted squares of Ricci tensors can be used to eliminate the anomaly completely. This peculiarity is discussed in detail. As tools we use the formalism of bisymmetric tensor fields whose space is equipped with a local bilinear invariant form, the *-form.