M Theory on AdS_p x S^{11-p} and Superconformal Field Theories

TL;DR

The paper investigates the spectra of chiral operators in the large $N$ limit of several 16-supercharge SCFTs arising from M-theory branes, via the proposed SCFT/$AdS$ duality. By computing Kaluza-Klein spectra on backgrounds $AdS_7 \times S^4$ and $AdS_4 \times S^7$ and mapping bulk modes to boundary operators using $m^2 = \Delta(\Delta-d)$ (scalars) and related relations for $p$-forms, it derives explicit operator dimensions for the $(0,2)$ 6D theories (including the $D_N$ orientifold) and the 3D ${\cal N}=8$ theories, in agreement with known DLCQ results where available. The results show that, at large $N$, only chiral primaries maintain finite dimensions, while non-chiral operators acquire dimensions that grow with $N$, highlighting a distinctive large $N$ structure and providing nonperturbative checks of M-theory/SCFT dualities in diverse dimensions. The work also clarifies how orientifold projections truncate spectra and how the moduli-space interpretations align with the KK spectra, contributing to a deeper understanding of holography beyond the familiar ${\cal N}=4$ SYM case.

Abstract

We study the large N limit of the interacting superconformal field theories associated with N M5 branes or M2 branes using the recently proposed relation between these theories and M theory on AdS spaces. We first analyze the spectrum of chiral operators of the 6d (0,2) theory associated with M5 branes in flat space, and find full agreement with earlier results obtained using its DLCQ description as quantum mechanics on a moduli space of instantons. We then perform a similar analysis for the D_N type 6d (0,2) theories associated with M5 branes at an R^5/Z_2 singularity, and for the 3d N=8 superconformal field theories associated with M2 branes in flat space and at an R^8/Z_2 singularity respectively. Little is known about these three theories, and our study yields for the first time their spectrum of chiral operators (in the large N limit).