On the quantization of the Abelian Chern-Simons coefficient at finite temperature

We show that when the Abelian Chern-Simons theory coupled to matter fields is quantized in a vacuum with nonvanishing magnetic flux (or electric charge), the requirement of gauge invariance at finite temperature leads to the quantization of the Chern-Simons coefficient and its quantum corrections, in a manner similar to the non-Abelian case.