Novel supermultiplets of SU(2,2|4) and the AdS_5/CFT_4 duality

TL;DR

This work refines the oscillator-based construction of unitary ${SU(2,2|4)}$ supermultiplets and clarifies the relation between compact and non-compact bases of ${SU(2,2)}$. It reaffirms that doubleton multiplets live on the AdS5 boundary and identifies a unique CPT self-conjugate ${N=4}$ Yang–Mills multiplet, while uncovering novel short non-doubleton multiplets with spin up to 2 that do not appear in standard KK spectra. These short multiplets can emerge from tensoring chiral doubletons and may relate to the massless limits of ${1/4}$ BPS states, potentially informing the solitonic sector of IIB strings on ${AdS_5 imes S^5}$ and guiding extensions of AdS/CFT toward ${SL(2,Z)}$-covariant string frameworks. Overall, the paper provides a powerful algebraic toolkit for linking AdS representations to 4D conformal supermultiplets and for exploring nonperturbative sectors of the AdS/CFT correspondence.

Abstract

We continue our study of the unitary supermultiplets of the N=8, d=5 anti-de Sitter (AdS_5) superalgebra SU(2,2|4), which is also the N=4 extended conformal superalgebra in d=4. We show explicitly how to go from the compact SU(2)XSU(2)XU(1) basis to the non-compact SL(2,C)XD basis of the positive energy unitary representations of the conformal group SU(2,2) in d=4. The doubleton representations of the AdS_5 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. The unique CPT self-conjugate irreducible doubleton supermultiplet of SU(2,2|4)is simply the 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 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 AdS_5 X S^5.