Effective action in a higher-spin background

TL;DR

This work analyzes a free massless scalar coupled to an infinite tower of background higher-spin gauge fields, formulating a non-Abelian unitary symmetry acting on the scalar and computing the gauge-invariant effective action via Schwinger proper-time regularization. The authors develop a perturbative heat-kernel framework, express the quadratic parts of both the finite and logarithmic (even-$d$) contributions in terms of higher-spin curvatures, and identify generalized HS Weyl anomalies; in even dimensions the logarithmic piece reproduces Segal's conformal HS gravity action, while in odd dimensions the finite part is nonlocal but gauge-invariant. They also relate the HS structure to standard lower-spin cases (electromagnetism and gravity) and discuss implications for AdS/CFT, including potential induced HS gravity dynamics and outstanding theoretical obstacles. Overall, the paper provides a detailed, curvature-based formulation of HS-induced effective actions and anomalies, highlighting both holographic connections and the technical challenges of constructing a fully consistent interacting HS gravity from a scalar see-saw.

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.