Probing AdS4/CFT3 proposals beyond chiral rings

TL;DR

This paper computes the superconformal index for a Chern-Simons-matter theory related to M2-branes and compares it with gravity dual predictions, revealing discrepancies at certain levels, thus probing the AdS4/CFT3 correspondence.

Contribution

It provides the first detailed superconformal index calculation for a specific M2-brane theory with N=3 supersymmetry and examines its consistency with gravity duals.

Findings

Disagreement between field theory index and gravity dual at k=1.

The model avoids exotic moduli space branches.

Supports the need for refined understanding of AdS4/CFT3 correspondence.

Abstract

We calculate the superconformal Witten index for the Chern-Simons-matter theory which was proposed to describe multiple M2-branes on $C^2 X C^2/Z_k$. We consider a variant of this model, which exhibits explicit N=3 supersymmetry and has the advantage of not having an exotic branch of the moduli space. At $k=1$, we compare the index with that from the proposed gravity dual and find a disagreement.