Yu. A. Tatarenko | Searcharxiv

arXiv2025

Bilinear higher-spin currents in the unfolded formalism

The classification of primary non-trivial bilinear currents in the 4d higher-spin theory is obtained. It is interpreted in terms of the known classification of cubic Lagrangian vertices in the 4d higher-spin theory. It is shown that some currents join to the action with the tail of higher-derivative terms (as it happens with the Fradkin-Vasiliev $2-s-s$ vertex). The analysis is based on the $σ_-$-cohomology technique of the unfolded formalism.

hep-th↗

arXiv2024

Bilinear Fronsdal currents in the $AdS_{4}$ 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 $ω$.

hep-th↗