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

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