Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant

TL;DR

This paper introduces a Monte Carlo method to study the ABJM theory for any N and coupling, enabling quantum-level tests of M-theory and duality predictions through numerical calculations of free energy.

Contribution

The paper presents a simple Monte Carlo approach to analyze the ABJM matrix model at arbitrary N and coupling, facilitating non-perturbative quantum investigations.

Findings

Confirmed N^{3/2} scaling in the M-theory limit

Interpolated between M-theory and type IIA regimes

Linked Fermi gas results to genus expansion contributions

Abstract

We show that the ABJM theory, which is an N=6 superconformal U(N)*U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy, and confirm the N^{3/2} scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models.