Branes, Orbifolds and the Three Dimensional ${\cal N} = 2$ SCFT in the Large N limit

TL;DR

This work studies the AdS$_4$/CFT$_3$ duality for ${\cal N}=2$ theories by embedding M-theory on orbifolds of $AdS_4 \times S^7$ and identifying a ${\bf C^3/Z_3}$ background via Brane Box Models and $(p,q)$-webs. It analyzes the KK spectrum of eleven-dimensional supergravity on the orbifold, projecting onto invariant states to extract the surviving chiral primary operators of the dual 3D SCFT in the untwisted sector. The proposed 3D theory has gauge group $SU(N)^3$ with bifundamental matter, and the surviving KK modes map to gauge-invariant operators such as ${\rm Tr}(U^iV^jW^k)$ and ${\rm Tr}(\Phi^i\widetilde{\Phi}_i)$ with dimensions fixed by the $U(1)_R$ charge. The work connects Brane Box Models with toric $(p,q)$-webs, laying groundwork for including twisted sectors via full M-theory and for generalizing to Calabi–Yau 4-fold compactifications.

Abstract

We study the correspondence between the large $N$ limit of ${\cal N} = 2$ three dimensional superconformal field theories and M theory on orbifolds of $AdS_4 \times {\bf S^7}$. We identify the brane configuration which gives $C^3/Z_3$ as a background for the M theory in terms of a Brane Box Model or a (p, q) web model. By taking the orbifold projection on the known spectrum of Kaluza-Klein harmonics of supergravity, we obtain information about the chiral primary operators at the orbifold singularities.