Bilinear Fronsdal currents in the AdS₄ higher-spin theory

We analyse higher-spin theory with general coupling constant η at the second order, focusing on the gauge non-invariant vertices Υ(ω, ω), Υ(Ω, ω, C) and Υ(ω, C), that are shown to generate nontrivial currents in the Fronsdal equations. Explicit expressions for the currents are found in the frame-like formalism counterpart of the TT gauge worked out in the paper. The nonlinear higher-spin theory is shown to generate all types of Metsaev’s currents with the coupling constants manifestly expressed via the complex coupling constant η of the higher-spin theory. It is shown that all currents in the higher-spin theory are conformal in the TT gauge except for those bilinear in the higher-spin gauge fields ω.