In a 2D CFT, correlation functions dominated by the vacuum block have no conical defects. You can calculate the OPE and determine the correlation function using the D-S equations and cancel out UV divergences with the Ward Id. However, with conical defects, you need to use a saddle point approximation in Gravitational theories like Chern-Simons. These are higher spin currents generated by conical defects.
My question is: What changes when you evaluate an OPE with correlation functions dominated by the conformal block and then evaluate conical defects using saddle point approximation action in gravity theories like Chern-Simons?