Refined test of AdS4/CFT3 correspondence for N=2,3 theories

TL;DR

This work systematically tests AdS$_4$/CFT$_3$ by computing and comparing superconformal indices for M2-branes on cones over $N^{010}/\mathbb{Z}_k$, $Q^{111}$, and $M^{32}$ with their gravity duals. For $N^{010}$ at $k=1$, the index matches exactly, and for general $k$ the D6-brane contributions from open strings into RP$^3$ sectors are crucial, illustrating the role of localized degrees of freedom beyond supergravity. In the $Q^{111}$ case, adding fundamental flavors to the $\mathcal{N}=6$ theory yields a gravity-consistent model with large-$N$ index agreement after careful treatment of certain multiplet towers. The $M^{32}$ analysis reveals partial agreement and highlights subtleties such as parity anomalies and unphysical saddle points, suggesting the need for model refinements. Collectively, the paper demonstrates both the power and the limitations of index-based AdS$_4$/CFT$_3$ tests in low-supersymmetry settings and points to directions for constructing fully consistent $\mathcal{N}=2$ dual pairs.

Abstract

We investigate the superconformal indices for the Chern-Simons-matter theories proposed for M2-branes probing the cones over N^{010}/Z_k, Q^{111}, M^{32} with N=2,3 supersymmetries and compare them with the corresponding dual gravity indices. For N^{010}, we find perfect agreements. In addition, for N^{010}/Z_k, we also find an agreement with the gravity index including the contributions from two types of D6-branes wrapping RP^3. For Q^{111}, we find that the model obtained by adding fundamental flavors to the N=6 theory has the right structure to be the correct model. For M^{32}, we find the matching with the gravity index modulo contributions from peculiar saddle points.

Figures (1)

• Figure 1: The quiver diagram of M2-branes on $C(M^{32})$