Effective action in a higher-spin background

TL;DR

This paper computes the gauge-invariant effective action for a scalar field coupled to an infinite set of higher-spin gauge fields, revealing connections to conformal higher-spin gravity and holography.

Contribution

It introduces a novel framework for coupling scalars to higher-spin fields with non-Abelian gauge symmetry and computes the resulting effective action, including anomalies and curvature structures.

Findings

Effective action expressed in terms of curvatures.

Identification of conformal higher-spin Weyl anomalies.

Connection to higher-spin gravity in AdS via holography.

Abstract

We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian group of unitary operators acting on the scalar field. The gauge invariant effective action is computed perturbatively in the external fields. The structure of the various (divergent or finite) terms is determined. In particular, the quadratic part of the logarithmically divergent (or of the finite) term is expressed in terms of curvatures and related to conformal higher-spin gravity. The generalized higher-spin Weyl anomalies are also determined. The relation with the theory of interacting higher-spin gauge fields on anti de Sitter spacetime via the holographic correspondence is discussed.