A note on vectorial AdS 5 /CFT 4 duality for spin- j boundary theory

The vectorial holographic correspondences between higher-spin theories in ads5 and free vector models on the boundary are extended to the cases where the latter is described by free massless spin-j field. the dual higher-spin theory in the bulk does not include gravity and can only be defined on rigid ads5 background with s 4 boundary. we discuss various properties of these rather special higher-spin theories and calculate their one-loop free energies. we show that the result is proportional to the same quantity for spin-j doubleton treated as if it is a ads5 field. finally, we consider even more special case where the boundary theory itself is given by an infinite tower of massless higher-spin fields.