Parity violating bosonic loops at finite temperature

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The finite temperature parity-violating contributions to the polarization tensor are computed at one loop in a system without fermions. The system studied is a Maxwell-Chern-Simons-Higgs system in the broken phase, for which the parity-violating terms are well known at zero temperature. At nonzero temperature the static and long-wavelength limits of the parity violating terms have very different structure, and involve nonanalytic log terms depending on the various mass scales. At high temperature the boson loop contribution to the Chern-Simons term goes like T in the static limit and like $T\mathrm{log}T$ in the long-wavelength limit, in contrast with the fermion loop contribution which behaves like $1/T$ in the static limit and like $\mathrm{log}T/T$ in the long wavelength limit.