Chern-Simons Theories on the Noncommutative Plane

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 κ=n/2π 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 κ+ρeθ=n/2π 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