The zeta function answer to parity violation in three-dimensional gauge theories

We study parity violation in (2 + 1)-dimensional gauge theories coupled to massive fermions. Using the zeta function regularization approach we evaluate the ground state fermion current in an arbitrary gauge field background, showing that it gets two different contributions which violate parity invariance and induce a Chern-Simons term in the gauge field effective action. One is related to the well-known classical parity breaking produced by a fermion mass term in three dimensions; the other, already present for massless fermions, is related to peculiarities of gauge-invariant regularization in odd-dimensional spaces.