The Chern–Simons term induced at high temperature and the quantization of its coefficient

Abstract

By perturbative calculations of the high-temperature ground-state axial vector current of fermion fields coupled to gauge fields, an anomalous Chern–Simons topological mass term is induced in the three-dimensional effective action. The anomaly in three dimensions appears just in the ground-state current rather than in the divergence of ground-state current. In the Abelian case, the contribution comes only from the vacuum polarization graph, whereas in the non-Abelian case, contributions come from the vacuum polarization graph and the two triangle graphs. The relation between the quantization of the Chern–Simons coefficient and the Dirac quantization condition of magnetic charge is also obtained. It implies that in a (2+1)-dimensional QED with the Chern–Simons topological mass term and a magnetic monopole with magnetic charge g present, the Chern–Simons coefficient must be also quantized, just as in the non-Abelian case.