TEMPERATURE-DEPENDENCE OF THE INDUCED CHERN-SIMONS TERM IN 2+1 DIMENSIONS

We study the temperature dependence of the,radiatively generated parity-breaking (Chern-Simons) term for massive fermions coupled to an external Abelian gauge held in 2+1 dimensions, using the imaginary time formalism. We allow the gauge field to be rapidly varying in space (as in a vortex, for example), and we also consider arbitrary discrete frequency components of the field. We thus go beyond the usual ''low momentum'' and ''adiabatic'' approximations. We give a simple analytical expression that is exact at both large and small momenta and provides a good interpolation at intermediate values. We also show under which conditions the usual adiabatic approximation is accurate, providing a simple physical picture for its prediction. Finally, we consider the same-problem for massless fermions coupled to a non-Abelian gauge held.