4D Doubleton Conformal Theories, CPT and IIB String on AdS_5 X S^5

TL;DR

This work classifies unitary supermultiplets of the $d=5$ AdS superalgebra $SU(2,2|4)$ using the oscillator method, with a complete enumeration of doubleton representations that live on the AdS$_5$ boundary and map to $d=4$ CFTs. The CPT self-conjugate doubleton corresponds to ${\cal N}=4$ super Yang-Mills in four dimensions, while other doubletons form CPT-conjugate pairs; massless reps arise from tensoring two doubletons and include the ${\cal N}=8$ graviton multiplet, with additional short multiplets up to spin 4. The paper then extends to general $SU(m,n|p+q)$, details the unitary supermultiplets of $SU(2,2|4)$, and presents explicit content for the doubleton and massless multiplets (Tables 1–12). In discussing CFT/AdS duality, the authors argue for a generalized duality where 4D ${\cal N}=4$ SYM couples to 4D ${\cal N}=4$ conformal supergravity, and highlight orbifold extensions and a deeper algebraic link between open and closed string sectors via the oscillator framework.

Abstract

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 AdS_5 X S^5. 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 AdS_5. 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 AdS_5. 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.