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arXiv · 1706.00047

Witten Diagrams for Torus Conformal Blocks

Per Kraus·Alexander Maloney·Henry Maxfield·Gim Seng Ng·Jie-qiang Wu
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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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Per Kraus, Alexander Maloney, Henry Maxfield, Gim Seng Ng, Jie-qiang Wu. 2017-05-31. Witten Diagrams for Torus Conformal Blocks. https://doi.org/10.1007/jhep09(2017)149

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