N=6 Supergravity on $AdS_5$ and the $SU(2,2/3)$ Superconformal Correspondence

TL;DR

This work links $N=6$ supergravity on $AdS_5$ with gauge group $SU(3)\times U(1)$ to a constrained subsector of $N=4$ SYM chiral primaries, via a duality-based projection at the self-dual coupling. It develops parallel truncations on the field theory and gravity sides: an $N=3$ truncation of $N=4$ SYM through a $U_1$ projection and an $N=8\to N=6$ truncation of the supergravity theory by retaining $U_1(1)$-singlets, yielding the $SU(3)\times U(1)$ gauged spectrum. The resulting massless content is captured by bilinears of the $N=3$ singleton $W_i$, producing the graviton and gravitino multiplets $G$ and $g$ consistent with the $N=6$ theory, while the Konishi multiplet remains and enforces OPE consistency. The paper also identifies selection rules for correlation functions that can be exact at the self-dual coupling and supports these results with AdS/CFT reasoning in the large-$N$ regime, highlighting a deep connection between CFT truncations and AdS gravity spectra.

Abstract

It is argued that N=6 supergravity on $AdS_5$, with gauge group $SU(3)\times U(1)$ corresponds, at the classical level, to a subsector of the ``chiral'' primary operators of N=4 Yang-Mills theories. This projection involves a ``duality transformation'' of N=4 Yang-Mills theory and therefore can be valid if the coupling is at a self-dual point, or for those amplitudes that do not depend on the coupling constant.