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Fujikawa's chiral rotation method is applied to calculate 3+1 dimensional chiral anomaly in many textbooks, but is there any counterpart of that method in deriving 2+1 dimensional parity anomaly, i.e. Chern-Simons action?

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    $\begingroup$ Parity anomaly is rather straightforward: for $2+1$ Dirac fermions, any regulator that preserves $U(1)$ must break time-reversal/parity symmetry. Pick such a regulator, integrating out the fermions, you get the Chern-Simons term. $\endgroup$ – Meng Cheng Apr 6 '15 at 2:52

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