Probing AdS4/CFT3 proposals beyond chiral rings

TL;DR

This work tests AdS$_4$/CFT$_3$ beyond chiral rings by computing the superconformal index for the ABJM theory and a closely related ${\rm N}=3$ variant. Using localization on $S^2\times S^1$ and monopole sectors, the authors show the ${\rm N}=3$ theory has a moduli space without exotic branches yet yields an index at $k=1$ that disagrees with the gravity dual, highlighting that identical moduli spaces do not guarantee dual CFTs. The calculation reveals a deconfinement-like behavior in the index at certain chemical potentials, with an apparent $N^2$ growth that challenges a simple M2-brane interpretation. These results underscore the subtle relationship between moduli space data, Witten indices, and holographic duals in 3d CS-matter theories, and suggest that moduli-space coincidences alone are insufficient to fix the dual gravity description.

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.