# Chern-Simons on a lattice and the framing anomaly

Can someone make or refer me to the argument for why $U(1)$ Chern-Simons theory in three dimensions cannot be defined by a lattice action? (Unlike Dijkgraaf-Witten theories, which are defined on the lattice.)

Possibly related: what is the "framing anomaly"?

• If one follow this paper, see formula $(6)$, the zero eigenvalues of the kernel (excluding zeroes due to translation invariance), define a set of planes (co-dimension $1$), the consequence being that the CS action is not integrable. Aug 25 '14 at 10:33