Chern-Simons Theories on Noncommutative Plane

Details Chern-Simons Theories on Noncommutative Plane Chern-Simons Theories on Noncommutative Plane

2001-02-27

arxiv.org/abs/hep-th/0102188v3

Phys.Rev.Lett. 87 (2001) 030402

Physics

High Energy Physics

High Energy Physics - Theory

revtex, two columns, 4 pages

Scientific paper

10.1103/PhysRevLett.87.030402

We investigate U(N) Chern-Simons theories on noncommutative plane. We show that for the theories to be consistent quantum mechanically, the coefficient of the Chern-Simons term should be quantized $\kappa = n/2\pi$ with an integer $n$. This is a surprise for the U(1) gauge theory. When uniform background charge density $\rho_e$ is present, the quantization rule changes to $\kappa +\rho_e\theta = n/2\pi$ with noncommutative parameter $\theta$. With the exact expression for the angular momentum, we argue in the U(1) theory that charged particles in the symmetric phase carry fractional spin $1/2n$ and vortices in the broken phase carry half-integer or integer spin $-n/2$.

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