Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory

Abstract

We analyse higher-spin theory with general coupling constant $\eta$ at the second order, focusing on the gauge non-invariant vertices ${\rm Y}(\omega ,\omega )$, ${\rm Y}(\Omega ,\omega ,C)$ and ${\rm Y}(\omega ,C)$, 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 $\eta$ 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 $\omega$.

47 pages; V2: minor corrections, acknowledgement added, matches the published version

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