Large N limit of the IKKT matrix model

Jul, 2000
20 pages
Published in:
  • Nucl.Phys.B 592 (2001) 391-407
e-Print:
Report number:
  • BI-TP-00-18,
  • BI-TP-2000-18

Citations per year

200020032006200920120246810
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 RR 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.
Note:
  • 20 pages, Latex + 9 eps figures, added references
  • lattice field theory
  • random surface: triangulation
  • supersymmetry
  • matrix model
  • string model
  • expansion 1/N
  • partition function: singularity
  • numerical calculations: Monte Carlo