Spontaneous parity breaking in three-dimensional non-Abelian gauge theory

We study the parity-odd part of the gauge field two-point function in the effective action in three-dimensional non-Abelian gauge theory with both Higgs fields and the Chern-Simons term. It is shown that, contrary to a previous proposal, there is no hint of spontaneous parity breakdown up to one-loop level, if care is taken to turn off the Chern-Simons coefficient before expanding the effective action into local terms. copyright 1996 The American Physical Society