Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations

The form of higher-spin current interactions in $AdS_4$ is derived from the full nonlinear higher-spin equations in the sector of Weyl 0-forms. The coupling constant in front of spin-one currents built from scalars and spinors as well as Yukawa coupling are determined explicitly. Couplings of all other higher-spin current interactions are determined implicitly. All couplings are shown to be independent of the phase parameter of the nonlinear higher-spin theory. The proper holographic dependence of the vertex on the higher-spin phase parameter is shown to result from the boundary conditions on the bulk fields.