Nonperturbative aspects of ABJM theory

TL;DR

This paper investigates non-perturbative effects in ABJM theory using matrix models, identifying instanton actions and confirming their role in the large N expansion, with a match to D2-brane instantons at strong coupling.

Contribution

It introduces a general method to extract spacetime instanton actions from matrix models via spectral curve periods and applies it to ABJM theory, revealing their physical interpretation.

Findings

Instanton actions are explicitly computed as functions of the 't Hooft coupling.

Numerical evidence shows instantons govern the asymptotic growth of the genus expansion.

The dominant instanton at strong coupling matches Euclidean D2-brane instantons wrapping RP^3.

Abstract

Using the matrix model which calculates the exact free energy of ABJM theory on S^3 we study non-perturbative effects in the large N expansion of this model, i.e., in the genus expansion of type IIA string theory on AdS4xCP^3. We propose a general prescription to extract spacetime instanton actions from general matrix models, in terms of period integrals of the spectral curve, and we use it to determine them explicitly in the ABJM matrix model, as exact functions of the 't Hooft coupling. We confirm numerically that these instantons control the asymptotic growth of the genus expansion. Furthermore, we find that the dominant instanton action at strong coupling determined in this way exactly matches the action of an Euclidean D2-brane instanton wrapping RP^3.