On the Superconformal Index of Chern-Simons theories and their KK Spectrometry

TL;DR

This paper compares the superconformal index of two 3D N=2 Chern-Simons theories at large N with their AdS/CFT duals, confirming the duality and refining the gravity index for one theory.

Contribution

It provides a detailed comparison of superconformal indices with KK spectra for mABJM and GJV theories, confirming the duality and refining the gravity index for enhanced symmetry.

Findings

Confirmed agreement between superconformal index and KK spectra for both theories.

Refined the gravity index for mABJM to account for enhanced global symmetry.

Validated the duality in the large-N limit for these theories.

Abstract

We study the large-$N$ limit of superconformal index for two strongly interacting Chern-Simons theories in three dimensions with $\mathcal{N}=2$ supersymmetry, and compare the result against the AdS/CFT dual, namely the data of full Kaluza-Klein reduction spectra obtained using the exceptional field theory technique. The two theories of interest are mABJM and GJV theories, which are obtained as IR fixed point of RG whose UV description is ABJM and maximally supersymmetric Yang-Mills theory respectively. We confirm agreement and the duality persists. For the case of mABJM it turns out that we need a refinement of the gravity index which reflects the fact that the UV description on the field theory side has enhanced global symmetry.