Ambitwistors, oscillators and massless fields on AdS5

Positive energy unitary irreducible representations of SU(2,2) can be constructed with the aid of bosonic oscillators in (anti)fundamental representation of SU(2)L×SU(2)R that are closely related to Penrose twistors. Starting with the correspondence between the doubleton representations, homogeneous functions on projective twistor space and on-shell generalized Weyl curvature SL(2,C) spinors and their low-spin counterparts, we study in the similar way the correspondence between the massless representations, homogeneous functions on ambitwistor space and, via the Penrose transform, with the gauge fields on Minkowski boundary of AdS5. The possibilities of reconstructing massless fields on AdS5 and some applications are also discussed.