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

We continue our study of the unitary supermultiplets of the 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 N = 4extended conformal superalgebra in d = 4. We show explicitly how to go from the compact SU(2) x SU(2) x U(1) basis to the non-compact SL(2, C) x 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 Poincare 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 cN = 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 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 x S5.