N. Bralic et al., ON THE QUANTIZATION OF THE ABELIAN CHERN-SIMONS COEFFICIENT AT FINITE-TEMPERATURE, Physics letters. Section B, 383(2), 1996, pp. 199-204
We show that when the Abelian Chem-Simons theory coupled to matter fie
lds is quantized in a vacuum with nonvanishing magnetic flux (or elect
ric charge), the requirement of gauge invariance at finite temperature
leads to the quantization of the Chern-Simons coefficient and its qua
ntum corrections, in a manner similar to the non-Abelian case.