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.

arXiv comment16 pages + appendix, 5 figures

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• Solving the Schwarzian via the Conformal Bootstrap
• A theory of reparameterizations for AdS${}_3$ gravity
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• Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs
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Cited by in corpus (1)

• Virasoro blocks and the reparametrization formalism