Large N limit of the IKKT matrix model Origin

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.