A Note on Instanton Effects in ABJM Theory

TL;DR

This paper investigates non-perturbative effects in the ABJM matrix model's quantum spectral problem, revealing new contributions to the grand potential through a Bohr-Sommerfeld quantization approach.

Contribution

It applies a method from previous work to determine non-perturbative contributions in the ABJM setting, highlighting higher order corrections beyond existing proposals.

Findings

Non-perturbative contributions to quantum phase volume are computed.

Higher order smooth corrections are identified beyond singularity cancellation.

Results suggest new contributions to the ABJM grand potential.

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.