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Noncommutative String Worldsheets from Matrix Models

K. N. Anagnostopoulos·J. Nishimura·P. Olesen
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Abstract

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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K. N. Anagnostopoulos, J. Nishimura, P. Olesen. 2001-01-30. Noncommutative String Worldsheets from Matrix Models. https://doi.org/10.1088/1126-6708%2F2001%2F04%2F024

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