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 AdS4. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter η=exp⁡iφ 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 ηη¯. Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at (η=0) η¯=0.