M Theory on the Stiefel manifold and 3d Conformal Field Theories

TL;DR

This work analyzes M-theory on $AdS_4\times V_{(5,2)}$ with $V_{(5,2)}=SO(5)/SO(3)$ to extract the dual 3d ${\cal N}=2$ SCFT data via AdS/CFT. The authors perform a complete harmonic KK analysis on the Stiefel coset, obtaining the mass spectrum through an $H_0(M,N,Q)$ eigenvalue and organizing states into ${\cal Osp(4|2)}$ multiplets, with no Betti multiplets, and they map these to boundary conformal operators, including protected chiral and semi-conserved operators. They propose a UV gauge theory $USp(2N)\times O(2N-1)$ with chiral singleton fields $S^i$ to describe parallel M2-branes at the conifold singularity, and they construct an explicit dictionary between KK states and CFT operators — e.g., short gravitino multiplets described by operators like $\mathrm{Tr}\,L_\alpha$ and $\mathrm{Tr}\,X_\alpha$. This study provides a concrete AdS$_4$/CFT$_3$ example on a non-toric Einstein manifold, offering a candidate Lagrangian UV completion and detailed operator matching that advances understanding of M2-brane CFT duals. $H_0(M,N,Q)$, $z^a$, and other key quantities are essential to the spectrum-operator correspondence.

Abstract

We compute the mass and multiplet spectrum of M theory compactified on the product of AdS(4) spacetime by the Stiefel manifold V(5,2)=SO(5)/SO(3), and we use this information to deduce via the AdS/CFT map the primary operator content of the boundary N=2 conformal field theory. We make an attempt for a candidate supersymmetric gauge theory that, at strong coupling, should be related to parallel M2-branes on the singular point of the non-compact Calabi-Yau four-fold $\sum_{a=1}^5 z_a^2 = 0$, describing the cone on V(5,2).