On short and long SU(2,2/4) multiplets in the AdS/CFT correspondence

TL;DR

The paper classifies short and long $SU(2,2|4)$ multiplets appearing in the OPE of chiral primaries in $N=4$ SYM within the AdS/CFT framework. It uses the oscillator construction to build long multiplets and analyzes their scalar content, providing explicit spectra for $J_{\max}=4,6,8$ and showing that only the Konishi-like long multiplet contains light scalars. It further decomposes long $n=4$ multiplets into $n=1$ supermultiplets, exemplified by the Konishi multiplet, clarifying the tower of $n=1$ representations that arise for $E_0=\ell$ up to $\ell+2$. The discussion extends to the structure of OPEs among KK, string, and supergravity states, highlighting the emergence of multilinear and multiparticle operators and a finite-$N$/stringy exclusion principle.

Abstract

We analyze short and long multiplets which appear in the OPE expansion of ``chiral'' primary operators in N=4 Super Yang--Mills theory. Among them, higher spin long and new short multiplets appear, having the interpretation, in the AdS/CFT correspondence, of string states and supergravity multiparticle states respectively. We also analyze the decomposition of long multiplets under N=1 supersymmetry, as a possible tool to explore other supersymmetric deformations of IIB string on AdS_5 x S_5.