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

TL;DR

This paper tests the AdS4/CFT3 correspondence for N=2,3 supersymmetric theories by comparing superconformal indices of specific M2-brane models with their gravity duals, confirming some cases and exploring others.

Contribution

It provides detailed comparisons of superconformal indices for several M2-brane theories, confirming the duality in certain models and analyzing contributions from branes and saddle points.

Findings

Perfect agreement for N^{010} case.

Agreement including D6-branes for N^{010}/Z_k.

Matching with gravity index for Q^{111} with added flavors.

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.