Noncommutative String Worldsheets from Matrix Models

Details Noncommutative String Worldsheets from Matrix Models Noncommutative String Worldsheets from Matrix Models

2000-12-07

arxiv.org/abs/hep-th/0012061v2

JHEP 0104:024,2001

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, 9 figures, JHEP.cls, added computation of Hausdorff dimension, references and minor corrections

Scientific paper

10.1088/1126-6708/2001/04/024

We study dynamical effects of introducing noncommutativity on string worldsheets by using a matrix model obtained from the zero-volume limit of four-dimensional SU($N$) Yang-Mills theory. Although the dimensionless noncommutativity parameter is of order 1/N, its effect is found to be non-negligible even in the large $N$ limit due to the existence of higher Fourier modes. We find that the Poisson bracket grows much faster than the Moyal bracket as we increase $N$, which means in particular that the two quantities do not coincide in the large $N$ limit. The well-known instability of bosonic worldsheets due to long spikes is shown to be cured by the noncommutativity. The extrinsic geometry of the worldsheet is described by a crumpled surface with a large Hausdorff dimension.

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