Large N limit of the IKKT matrix model

TL;DR

This study numerically investigates the large N limit of the four-dimensional IKKT matrix model, demonstrating how supersymmetry suppresses pathological configurations and analyzing the distribution of the gyration radius.

Contribution

It provides a numerical analysis of the supersymmetric random surface model related to the IKKT matrix model, revealing the effects of fermionic degrees of freedom on the model's behavior.

Findings

Fermionic degrees of freedom suppress spiky configurations.

Distribution of gyration radius follows a power-law tail p(R) ~ R^{-2.4}.

Supersymmetry leads to a well-defined model with a one-dimensional tube structure.

Abstract

Using the dynamical triangulation approach we perform a numerical study of a supersymmetric random surface model that corresponds to the large N limit of the four-dimensional version of the IKKT matrix model. We show that the addition of fermionic degrees of freedom suppresses the spiky world-sheet configurations that are responsible for the pathological behaviour of the purely bosonic model. We observe that the distribution of the gyration radius has a power-like tail p(R) ~ R^{-2.4}. We check numerically that when the number of fermionic degrees of freedom is not susy-balanced, p(R) grows with $R$ and the model is not well-defined. Numerical sampling of the configurations in the tail of the distribution shows that the bosonic degrees of freedom collapse to a one-dimensional tube with small transverse fluctuations. Assuming that the vertex positions can fluctuate independently within the tube, we give a theoretical argument which essentially explains the behaviour of p(R) in the different cases, in particular predicting p(R) ~ R^{-3} in the supersymmetric case. Extending the argument to six and ten dimensions, we predict p(R) ~ R^{-7} and p(R) ~ R^{-15}, respectively.