Witten Diagrams for Torus Conformal Blocks

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.

arXiv comment32 pages, 6 figures

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Cited by in corpus (32)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Semiclassical 3D gravity as an average of large-c CFTs
• The Conformal Bootstrap at Finite Temperature
• Universal Dynamics of Heavy Operators in CFT${}_2$
• Probing thermality beyond the diagonal
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• Quasi-local holographic dualities in non-perturbative 3d quantum gravity
• Holographic OPE Coefficients from AdS Black Holes with Matters
• Thermal Conformal Blocks
• A multipoint conformal block chain in $d$ dimensions
• Holographic duals of large-c torus conformal blocks
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• Chaos in CFT dual to rotating BTZ
• Towards Feynman rules for conformal blocks
• Holographic torus correlators of stress tensor in $Ad{S}_3/CF{T}_2$
• Fermions in Geodesic Witten Diagrams
• Scalar Blocks as Gravitational Wilson Networks
• Structure Constants from Modularity in Warped CFT
• Phase transitions in 3D gravity and fractal dimension
• Large-c superconformal torus blocks
• More on Wilson toroidal networks and torus blocks
• BMS Modular Diaries: Torus one-point function
• Toward the Pole
• Semiclassical torus blocks in the t-channel
• A view of the bulk from the worldline
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• Rényi entropy of single-character CFTs on the torus