On holomorphic sector of higher-spin theory

Recent investigation of the locality problem for higher-spin fields led to a vertex reconstruction procedure that involved elements of contraction of the original Vasiliev interaction algebra. Inspired by these results we propose the Vasiliev-like generating equations for the holomorphic higher-spin interactions in four dimensions based on the observed contracted algebra. We specify the functional class that admits evolution on the proposed equations and brings in a systematic procedure of extracting all-order holomorphic vertices. A simple consequence of the proposed equations is the space-time locality of the gauge field sector. We also show that vertices come with a remarkable shift symmetry.