The structure of the trace anomaly of higher spin conformal currents in the bulk of $AdS_{4}$

TL;DR

This paper analyzes the trace anomaly of higher spin conformal currents in AdS4, deriving the structure of the anomaly and the quadratic effective action, including known results for the spin-2 (gravitational) case.

Contribution

It provides a detailed calculation of the trace anomaly for higher spin currents in AdS4 and explicitly constructs the quadratic effective action, extending known results for spin-2.

Findings

Trace anomaly arises only in the trace part of the two-point function.

Explicit form of the quadratic effective action for the trace of higher spin fields.

Reproduction of known results for the spin-2 (gravitational) case.

Abstract

The two-point function of the conserved traceless spin-$\ell$ currents which are constructed from the scalar field $\sigma(z)$ is evaluated and renormalized by a dimensional regularization procedure. The anomaly is managed to arise only in the trace part. To isolate this trace anomaly it is sufficient to analyze only the maximum singular part of the two-point function and its trace terms to leading order. The corresponding part of the effective action which is quadratic in the trace of the higher spin field is explicitly given. For the spin-2 field which is identical with the gravitational field the results known from the literature are reproduced.