TEMPERATURE-DEPENDENCE OF THE INDUCED CHARGE-DENSITY IN THE PRESENCE OF A MAGNETIC-FLUX STRING IN 2+1 DIMENSIONS

We study the temperature dependence of the induced charge density in three-dimensional QED with massive fermions coupled to a static external magnetic flux string. This effect is due to the parity-violating part of the effective action. Using a previous result for the induced Chern-Simons term at finite temperature, which is a reliable approximation even for problems where the gauge field has strong variations, we explicitly calculate the induced charge density at finite temperature in analytical form, and the existence of an induced charge at infinity is easily demonstrated. Our results for the zero temperature case agree with the previous calculations in the case of weak coupling, and for a nonzero temperature we verify that our result for the total charge agrees with the prediction of the corresponding (exact) trace identity.