4D doubleton conformal theories, CPT and IIB strings on AdS5 × S5

We study the unitary supermultiplets of the N = 8 d = 5 anti-de Sitter (AdS) superalgebra SU(2, 2|4) which is the symmetry algebra of the IIB string theory on AdS5 × S5. We give a complete classification of the doubleton supermultiplets of SU(2, 2|4) which do not have a Poincare limit and correspond to d = 4 conformal field theories (CFT) living on the boundary of AdS5. The CPT self-conjugate irreducible doubleton supermultiplet corresponds to d = 4 N = 4 super Yang-Mills theory. The other irreducible doubleton supermultiplets come in CPT conjugate pairs. The maximum spin range of the general doubleton supermultiplets is 2. In particular, there exists a CPT conjugate pair of doubleton supermultiplets corresponding to the fields of N = 4 conformal supergravity in d = 4 which can be coupled to N = 4 super Yang-Mills theory in d = 4. We also study the “massless” supermultiplets of SU(2, 2|4) which can be obtained by tensoring two doubleton supermultiplets. The CPT self-conjugate “massless” supermultiplet is the N = 8 graviton supermultiplet in AdS5. The other “massless” supermultiplets generally come in conjugate pairs and can have maximum spin range of 4. We discuss the implications of our results for the conjectured CFT/AdS dualities.