Conformal Blocks and Bilocal Vertex Operator Transition Amplitudes

Abstract

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 Kähler quantization of virasoro coadjoint orbits, $SL(2,\mathbb{R})$ Chern-Simons theory and the reparametrization formalism of 2d CFT that has made an appearance in recent literature.

16 pages + appendix, 5 figures

References in corpus (2)

• On the Virasoro six-point identity block and chaos
• Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges

Cited by in corpus (1)

• Virasoro blocks and the reparametrization formalism