Novel supermultiplets of SU(2,2/4) and the AdS₅/CFT₄ duality

We continue our study of the unitary supermultiplets of the script N = 8 d = 5 anti-de Sitter (AdS₅) superalgebra SU(2, 2/4), which is the symmetry algebra of type IIB superstring theory on AdS₅ × S⁵. SU(2,2/4) is also the script N = 4 extended conformal superalgebra in d = 4. We show explicitly how to go from the compact SU(2) × SU(2) × U(1) basis to the non-compact SL(2, ℂ) × D basis of the positive (conformal) energy unitary representations of the conformal group SU(2, 2) in d = 4. The doubleton representations of the AdS₅ group SU(2, 2), which do not have a smooth Poincaré limit in d = 5, are shown to represent fields with vanishing masses in four-dimensional Minkowski space, i.e. on the boundary of AdS₅, where SU(2, 2) acts as conformal group. The unique CPT self-conjugate irreducible doubleton supermultiplet of SU(2, 2/4) is simply the script N = 4 Yang-Mills supermultiplet in d = 4. We study some novel short non-doubleton supermultiplets of SU(2, 2/4) that have spin range 2 and that do not appear in the Kaluza-Klein spectrum of type IIB supergravity or in tensor products of the script N = 4 Yang-Mills supermultiplet with itself. These novel supermultiplets can be obtained from tensoring chiral doubleton supermultiplets,some of which we expect to be related to the massless limits of 1/4 BPS states. Hence, these novel supermultiplets may be relevant to the solitonic sector of IIB superstring and/or (p,q) superstrings over AdS₅ × S⁵.