0 v 2 1 2 N ov 2 00 1 Induced parity violating thermal effective action for 2 + 1 - dimensional fermions interacting with a non - Abelian background

We study the parity breaking effective action in 2 + 1 dimensions, generated, at finite temperature, by massive fermions interacting with a non-Abelian gauge background. We explicitly calculate, in the static limit, parity violating amplitudes up to the seven point function, which allows us to determine the corresponding effective actions. There are two classes of such actions that arise, namely, terms that do not manifestly depend on ~ E and ones that do. We derive the exact effective action that is not manifestly dependent on ~ E. For the other class that depends explicitly on ~ E, there are families of terms that can be determined order by order in perturbation theory. We attempt to generalize our results to non-static backgrounds through the use of time ordered exponentials and prove gauge invariance, both small and large, of the resulting effective action. We also point out some open questions that need to be further understood.