Conformal blocks and bilocal vertex operator transition amplitudes. (English) Zbl 1522.81541
Summary: 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, \(\mathrm{SL}(2, \mathbb{R})\) Chern-Simons theory and the reparametrization formalism of 2d CFT that has made an appearance in recent literature.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 81T70 | Quantization in field theory; cohomological methods |
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