Large N limit of the IKKT matrix model
Jul, 2000
20 pages
Published in:
- Nucl.Phys.B 592 (2001) 391-407
e-Print:
- hep-lat/0007013 [hep-lat]
Report number:
- BI-TP-00-18,
- BI-TP-2000-18
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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 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
References(30)
Figures(0)