Parity-violating electromagnetic interactions in three-dimensional QED at finite temperature

We study the parity-breaking terms generated by the box diagram in (2+1)-dimensional thermal QED. These lead, in the long;wave limit, to a gauge invariant extensive action, which behaves as 1/T at high temperature. In contrast, the effective action in the static limit involves leading nonextensive terms proportional to 1/T-3 at high temperature, which violate large gauge invariance. We derive a nonlinear large gauge Ward identity, which relates the leading static terms of different order in perturbation theory and whose solution coincides with the all order effective action proposed earlier.