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arXiv · hep-th/0102188

Chern-Simons Theories on Noncommutative Plane

Dongsu Bak·Kimyeong Lee·Jeong-Hyuck Park
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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 $κ= n/2π$ with an integer $n$. This is a surprise for the U(1) gauge theory. When uniform background charge density $ρ_e$ is present, the quantization rule changes to $κ+ρ_eθ= n/2π$ with noncommutative parameter $θ$. 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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Dongsu Bak, Kimyeong Lee, Jeong-Hyuck Park. 2001-03-20. Chern-Simons Theories on Noncommutative Plane. https://doi.org/10.1103/physrevlett.87.030402

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