Instanton Effects in Orbifold ABJM Theory

Abstract

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.

23 pages, 2 eps figures; v2: minor improvements

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Cited by in corpus (9)

• Probing non-perturbative effects in M-theory
• Exact results on ABJ theory and the refined topological string
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• ABJ Wilson loops and Seiberg Duality
• Ward and Nielsen Identities for ABJM Theory in $\mathcal{N}=1$ Superspace