Noncommutative String Worldsheets from Matrix Models

TL;DR

This paper investigates how noncommutativity affects string worldsheets using matrix models derived from SU(N) Yang-Mills theory, revealing that noncommutativity stabilizes worldsheets and alters their geometric properties even at large N.

Contribution

It demonstrates that noncommutativity significantly influences string worldsheet dynamics and geometry, especially by stabilizing worldsheets and changing their extrinsic curvature behavior.

Findings

Noncommutativity stabilizes bosonic worldsheets against long spike instabilities.

Poisson and Moyal brackets diverge as N increases, indicating different large N limits.

Worldsheets become crumpled with high Hausdorff dimension due to noncommutativity.

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.