Bilinear Fronsdal currents in the $AdS_{4}$ higher-spin theory

TL;DR

This paper investigates the structure of currents in the $AdS_{4}$ higher-spin theory at second order, providing explicit expressions and demonstrating their conformal properties in a specific gauge.

Contribution

It derives explicit forms of gauge non-invariant currents in higher-spin theory and shows their relation to Metsaev's currents with a complex coupling constant.

Findings

All types of Metsaev's currents are generated with explicit coupling constants.

Currents are conformal in the TT gauge, except for bilinear higher-spin gauge field currents.

Explicit expressions for currents are obtained in the frame-like formalism.

Abstract

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