# Fujikawa's method for 2+1-dimensional parity anomaly?

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?

• 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. – Meng Cheng Apr 6 '15 at 2:52