Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions

TL;DR

This paper develops a systematic method to derive conserved currents and cubic interactions between scalar fields and higher-spin gauge fields on constant curvature spacetimes, extending flat space results via dimensional reduction.

Contribution

It introduces a unified approach to construct conserved currents and cubic couplings for higher-spin fields interacting with scalars on (A)dS spaces using generating functions and Weyl/Wigner quantization.

Findings

Derived conserved currents for all ranks from flat space counterparts.

Presented a compact generating function formalism for interactions.

Validated the approach within the unitarity mass-square domain.

Abstract

Cubic couplings between a complex scalar field and a tower of symmetric tensor gauge fields of all ranks are investigated on any constant curvature spacetime of dimension d>2. Following Noether's method, the gauge fields interact with the scalar field via minimal coupling to the conserved currents. A symmetric conserved current, bilinear in the scalar field and containing up to r derivatives, is obtained for any rank r from its flat spacetime counterpart in dimension d+1, via a radial dimensional reduction valid precisely for the mass-square domain of unitarity in (anti) de Sitter spacetime of dimension d. The infinite collection of conserved currents and cubic vertices are summarized in a compact form by making use of generating functions and of the Weyl/Wigner quantization on constant curvature spaces.