Abstract
We give a holographic description of global conformal blocks in two dimensional conformal field theory on the sphere and on the torus. We show that the conformal blocks for one-point functions on the torus can be written as Witten diagrams in thermal AdS. This is accomplished by deriving a general conformal Casimir equation for global conformal blocks, and showing that Witten diagrams obey the same equation. We study the semi-classical limit of n-point conformal blocks, and show that these equal the action of a network of bulk world-lines obeying appropriate geodesic equations. We give an alternate description in the Chern-Simons formulation of 3D gravity, where the conformal blocks are described by networks of Wilson lines, and argue that these formulations are equivalent.
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ArXiv ePrint: 1706.00047
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Kraus, P., Maloney, A., Maxfield, H. et al. Witten diagrams for torus conformal blocks. J. High Energ. Phys. 2017, 149 (2017). https://doi.org/10.1007/JHEP09(2017)149
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DOI: https://doi.org/10.1007/JHEP09(2017)149