First of, if any of the following below does not make sense, please feel free to leave a comment =)
Central charges in Chern Simons in in the Virasoro conformal blocks play an important role for generating Conformal and Lorentz anomalies as non-local modes. In Chern Simons, a flat Holonomy corresponds to a vanishing Monodromy. I was wondering if there was any way to connect central charges with the representations of the spin structure. If so, does that mean the irreducible represents of the spin structure with a non-flat Holonomy can be regarded as the non-local modes generating the various anomalies above.