# Large N limit of the IKKT matrix model

Bialas P, Burda Z, Petersson B, Tabaczek J (2001)

NUCLEAR PHYSICS B 592(1-2): 391-407.

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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) similar to 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) similar to R-3 in the supersymmetric case. Extending the argument to six and ten dimensions, we predict p(R) similar to R-7 and p(R) similar to R-15 respectively. (C) 2001 Elsevier Science B.V. All rights reserved.

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Bialas P, Burda Z, Petersson B, Tabaczek J. Large N limit of the IKKT matrix model.

*NUCLEAR PHYSICS B*. 2001;592(1-2):391-407.Bialas, P., Burda, Z., Petersson, B., & Tabaczek, J. (2001). Large N limit of the IKKT matrix model.

*NUCLEAR PHYSICS B*,*592*(1-2), 391-407. doi:10.1016/S0550-3213(00)00583-6Bialas, P., Burda, Z., Petersson, B., and Tabaczek, J. (2001). Large N limit of the IKKT matrix model.

*NUCLEAR PHYSICS B*592, 391-407.Bialas, P., et al., 2001. Large N limit of the IKKT matrix model.

*NUCLEAR PHYSICS B*, 592(1-2), p 391-407. P. Bialas, et al., “Large N limit of the IKKT matrix model”,

*NUCLEAR PHYSICS B*, vol. 592, 2001, pp. 391-407. Bialas, P., Burda, Z., Petersson, B., Tabaczek, J.: Large N limit of the IKKT matrix model. NUCLEAR PHYSICS B. 592, 391-407 (2001).

Bialas, P, Burda, Z, Petersson, Bengt, and Tabaczek, J. “Large N limit of the IKKT matrix model”.

*NUCLEAR PHYSICS B*592.1-2 (2001): 391-407.
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