Chern-Simons Theories on the Noncommutative Plane

Dongsu Bak, Kimyeong Lee, Jeong Hyuck Park

Research output: Contribution to journalArticlepeer-review


We investigate 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 k = n/2 π with an integer n. This is a surprise for the U(1) gauge theory. When uniform background charge density ρe is present, the quantization rule changes to k + ρeθ = n/2 π with the 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.

Original languageEnglish
Pages (from-to)30402-1-30402-4
JournalPhysical Review Letters
Issue number3
StatePublished - 16 Jul 2001


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