On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field

We propose field equations for the conformal higher spin system in three dimensions coupled to a conformal scalar field with a sixth order potential. both the higher spin equation and the unfolded equation for the scalar field have source terms and are based on a conformal higher spin algebra which we treat as an expansion in multi-commutators. explicit expressions for the source terms are suggested and subjected to some simple tests. we also discuss a cascading relation between the chern-simons action for the higher spin gauge theory and an action containing a term for each spin that generalizes the spin 2 chern-simons action in terms of the spin connection expressed in terms of the frame field. this cascading property is demonstrated in the free theory for spin 3 but should work also in the complete higher spin theory.