Noncommutative String Worldsheets from Matrix Models

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.

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

References in corpus (3)

• Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory
• Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model
• Large N Structure of the IIB Matrix Model

Cited by in corpus (7)

• Quantum Field Theory on Noncommutative Spaces
• On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings
• The Area Law in Matrix Models for Large N QCD Strings
• Lattice Superstring and Noncommutative Geometry
• Large-N behaviors of the IIB matrix model and the regularized Schild models
• Representation of SU(infinity) Algebra for Matrix Models
• A regularization of field theory on non-commutative torus