Conformal blocks and bilocal vertex operator transition amplitudes

A bstract We revisit the construction of 2d conformal blocks primary operator four-point functions as bilocal vertex correlators. find an additional interpretation a path integral over reparametrizations intermediate cylinder. As consequence we bridge gap between Kähler quantization virasoro coadjoint orbits, SL(2 , ?) Chern-Simons theory and reparametrization formalism CFT that has made appearance in recent literature.