Conformal blocks and bilocal vertex operator transition amplitudes

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

Automated summary

In this study, we revisit the construction of primary operator four-point functions and provide an additional interpretation as a path integral over the reparametrizations of an intermediate cylinder. This approach bridges the gap between different research fields and provides a more complete understanding of the topic.