Induced Chern-Simons Terms at High Temperatures and Finite Densities

The CP-nonconserving portion of the gauge-field effective action for an even number of left-handed SU(2) fermion doublets, with nonzero chemical potentials μⁱ, is calculated to leading order in the inverse temperature, T^-1. It is shown to be ⁱΣᵢ(μⁱT)W[A], where $W[A]$ is the Chern-Simons topological mass term. This result is also shown to be a consequence of the U(1)L anomaly at zero temperature, but with μ≠0. Because of the i in front of the Chern-Simons term, this produces magnetic screening only if μ is complex.