Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations

The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in $AdS_4$. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter $eta =exp ivarphi$ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant $etabareta$. Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at ($eta=0$) $bar eta=0$.