Instanton Effects in Orbifold ABJM Theory

We study the partition function of the orbifold ABJM theory on $S^3$, which is the $\mathcal{N}=4$ necklace quiver Chern-Simons-matter theory with alternating levels, in the Fermi gas formalism. We find that the grand potential of the orbifold ABJM theory is expressed explicitly in terms of that of the ABJM theory. As shown previously, the ABJM grand potential consists of the naive but primary non-oscillatory term and the subsidiary infinitely-replicated oscillatory terms. We find that the subsidiary oscillatory terms of the ABJM theory actually give a non-oscillatory primary term of the orbifold ABJM theory. Also, interestingly, the perturbative part in the ABJM theory results in a novel instanton contribution in the orbifold theory. We also present a physical interpretation for the non-perturbative instanton effects.