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

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.