A Note on Instanton Effects in ABJM Theory

Abstract

We consider the quantum spectral problem appearing the Fermi gas formulation of the ABJM (Aharony-Bergman-Jafferis-Maldacena) matrix model. This is known to related to the refined topological string on local P^1*P^1 Calabi-Yau geometry. In the ABJM setting the problem is formulated by an integral equation, and is somewhat different from the one formulated directly in terms of the Calabi-Yau geometry and studied in our earlier paper. We use the similar method in our earlier paper to determine the non-perturbative contributions to the quantum phase volume in the ABJM case from the Bohr-Sommerfeld quantization condition. As in our earlier paper, the non-perturbative contributions contain higher order smooth corrections beyond those required by singularity cancellations with the perturbative contributions proposed by Kallen and Marino. Our results imply possible new contributions to the grand potential of the ABJM matrix model.

18 pages

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Cited by in corpus (7)

• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Localization at large N in Chern-Simons-matter theories
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
• Geometric transition in Non-perturbative Topological string