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

35+1 pages, v2: two references added, typos corrected, enlarged discussions in Subsection 5.2 and in Conclusion, to appear in JHEPInternational audienceCubic 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