Holographic conformal blocks from interacting Wilson lines

Abstract

We present a simple prescription for computing conformal blocks and correlation functions holographically in AdS${}_3$ in terms of Wilson lines merging at a bulk vertex. This is shown to reproduce global conformal blocks and heavy-light Virasoro blocks. In the case of higher spin theories the space of vertices is in one-to-one correspondence with the space of ${\mathcal{W}}_N$ conformal blocks, and we show how the latter are obtained by explicit computations.

arXiv comment40 pages, 1 figure

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• On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles
• Holographic dual of the five-point conformal block
• Witten Diagrams for Torus Conformal Blocks
• Degenerate Operators and the $1/c$ Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks
• Conformal blocks from Wilson lines with loop corrections
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• A multipoint conformal block chain in $d$ dimensions
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Wilson Lines and Ishibashi States in AdS${}_3$/CFT${}_2$
• Renormalization of gravitational Wilson lines
• Keeping matter in the loop in dS${}_3$ quantum gravity
• Towards Feynman rules for conformal blocks
• Scalar Blocks as Gravitational Wilson Networks
• A note on the Virasoro blocks at order $1/c$
• Superconformal blocks from Wilson lines with loop corrections
• Gravitational Wilson Lines in 3D de Sitter
• Bands and gaps in Nekrasov partition function
• Late time Wilson lines
• Local quenches and quantum chaos from higher spin perturbations
• Geodesic description of Heavy-Light Virasoro blocks
• More on Wilson toroidal networks and torus blocks
• Multi-centered higher spin solutions from $W_N$ conformal blocks
• Wilson line networks in $p$-adic AdS/CFT
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Semi-classical BMS-blocks from the Oscillator Construction
• On scalar propagators of three-dimensional higher-spin black holes