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.