Chern–Simons quantum field theory on a closed oriented 3-manifold M exhibits a framing anomaly:the quantum partition function is not canonically a complex number, but is naturally valued in acomplex line that depends on a choice of 2-framing. We recast the framing anomaly as the holonomyof a flat unitary line bundle over the integer 2-framing torsor, in the sense that for the unit shift onehasZ(M,f +1) =exp 2πi24 c(G,k) Z(M,f).(1)The dependence is discrete yet rigid, controlled by the effective central charge c(G,k). We state aprecise theorem in a minimal functorial topological quantum field theory (TQFT) language andpresent an explicit SU(2)k check on S3, with a self-contained surgery derivation deferred to Section A.
SIKX HILTON (Fri,) studied this question.