Year: 2001
Type: article
Abstract: We investigate $\mathrm{U}(N)$ Chern-Simons theories on the noncommutative plane. We show that for the theories to be consistent quantum mechanically, the coefficient of the Chern-Simons term should be quantized $\ensuremath{\kappa}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n/2\ensuremath{\pi}$ with an integer $n$. This is a surprise for the $\mathrm{U}(1)$ gauge theory. When uniform background charge density ${\ensuremath{\rho}}_{e}$ is present, the quantization rule changes to $\ensuremath{\kappa}+{\ensuremath{\rho}}_{e}\ensuremath{\theta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n/2\ensuremath{\pi}$ with the noncommutative parameter $\ensuremath{\theta}$. With the exact expression for the angular momentum, we argue in the $\mathrm{U}(1)$ 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 $\ensuremath{-}n/2$.
Source: Physical Review Letters
Authors: Dongsu Bak, Kimyeong Lee, Jeong-Hyuck Park
Institutions: University of Seoul, Korea Institute for Advanced Study
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G1179514175
OpenAlex ID: W2071906262