Three Dimensional SCFT from M2 Branes at Conifold Singularities

TL;DR

The paper addresses the problem of identifying a three-dimensional SCFT dual to M-theory on $AdS_4 \times Q^{1,1,1}$ by studying M2 branes at a conifold singularity and exploiting a self-mirror duality in three dimensions. It constructs the horizon geometry $Q^{1,1,1}$ as the link of a Calabi–Yau canonical singularity $Y$, relates it to a complex blow-up of a related orbifold, and derives a $U(N) \times U(N)$ gauge theory with bifundamental matter that flows to an IR fixed point; this fixed point is then shown to be connected by a marginal deformation to the conifold theory, yielding the proposed $AdS_4 \times Q^{1,1,1}$ holographic dual. Key contributions include a concrete 3d $\mathcal{N}=2$ field theory realizing the conifold moduli, a marginal operator connecting fixed points, and a geometric/topological bridge to the orbifold/blow-up picture, enriching the landscape of AdS4/CFT3 with Sasaki–Einstein horizons. The work advances understanding of how M2-brane dynamics at conifold-like singularities encode 3d SCFTs and their holographic descriptions, with potential implications for constructing and classifying such dual pairs.

Abstract

Recently it was conjectured that parallel branes at conical singularities are related to string/M theory on $AdS \times X$ where $X$ is an Einstein manifold. In this paper we consider coincident M2 branes near a conifold singularity when M theory is compactified on $AdS_4 \times Q^{1,1,1}$ where $Q^{1,1,1} = (SU(2) \times SU(2) \times SU(2))/(U(1) \times U(1))$ is a seven dimensional Sasaki-Einstein manifold. We argue that M theory on $AdS_4 \times Q^{1,1,1}$ can be described in terms of a three dimensional superconformal field theory.We use the fact that the three dimensional self-mirror duality is preserved by exact marginal operators, as observed by Strassler.