Chern-Simons Theories on Noncommutative Plane

Abstract

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 $-n/2$.

arXiv commentrevtex, two columns, 4 pages

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