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

Abstract

We analyse higher-spin theory with general coupling constant $\hat{I}\cdot$ at the second order, focusing on the gauge non-invariant vertices $\hat{I}\yen (\ddot{I}‰,\ddot{I}‰)$, $\hat{I}\yen (\hat{I}\text{c◯},\ddot{I}‰,C)$ and $\hat{I}\yen (\ddot{I}‰,C)$, 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 $\hat{I}\cdot$ 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 $\ddot{I}‰$.

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