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 $\eta =\exp i\varphi$ 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 $\eta\bar\eta$. Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at ($\eta=0$) $\bar \eta=0$.Comment: 38 pages, no figures; V2: 39 pages, minor corrections, to be published versio