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.

40 pages, 1 figure

References in corpus (7)

• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Symmetries of Holographic Minimal Models
• Higher-point conformal blocks and entanglement entropy in heavy states
• Holographic Conformal Partial Waves as Gravitational Open Wilson Networks
• Eternal Higher Spin Black Holes: a Thermofield Interpretation

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