Tests of AdS$_4$/CFT$_3$ correspondence for $\mathcal{N}=2$ chiral-like theory

TL;DR

This paper verifies the AdS$_4$/CFT$_3$ correspondence for a specific $ ext{N}=2$ chiral-like theory by matching field theory calculations with gravity predictions, confirming the duality's validity.

Contribution

It provides the first detailed comparison of superconformal index and partition function for this chiral-like theory with its gravity dual.

Findings

Superconformal index matches gravity index

Partition function agrees with gravitational free energy

Supports the AdS$_4$/CFT$_3$ duality for this model

Abstract

We investigate the superconformal index and the partition function for the chiral-like Chern-Simons-matter theory proposed for M2-branes probing the cones over $M^{3,2}$ and find perfect agreements with the gravity index and the gravitational free energy.