Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex

TL;DR

This paper constructs the cubic interaction vertices for higher-spin gauge fields coupled with scalars using a BRST approach, highlighting differences between flat space and AdS, with implications for holography.

Contribution

It introduces a BRST-based method to derive cubic vertices for higher-spin fields interacting with scalars, including new vertices in AdS space and an alternative derivation approach.

Findings

Constructed cubic vertices for higher-spin triplets in flat space.

Identified additional interaction vertices in AdS space.

Connected higher-spin gauge fields to higher derivative symmetries of matter Lagrangians.

Abstract

We apply a recently presented BRST procedure to construct the Largangian cubic vertex of higher-spin gauge field triplets interacting with massive free scalars. In flat space, the spin-s triplet propagates the series of irreducible spin-s, s-2,..,0/1 modes which couple independently to corresponding conserved currents constructed from the scalars. The simple covariantization of the flat space result is not enough in AdS, as new interaction vertices appear. We present in detail the cases of spin-2 and spin-3 triplets coupled to scalars. Restricting to a single irreducible spin-s mode we uncover previously obtained results. We also present an alternative derivation of the lower spin results based on the idea that higher-spin gauge fields arise from the gauging of higher derivative symmetries of free matter Lagrangians. Our results can be readily applied to holographic studies of higher-spin gauge theories.