Holographic Conformal Partial Waves as Gravitational Open Wilson Networks

Abstract

We propose a method to holographically compute the conformal partial waves in any decomposition of correlation functions of primary operators in conformal field theories using open Wilson network operators in the holographic gravitational dual. The Wilson operators are the gravitational ones where gravity is written as a gauge theory in the first order Hilbert-Palatini formalism. We apply this method to compute the global conformal blocks and partial waves in 2d CFTs reproducing many of the known results.

arXiv comment33 pages, 5 figures

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• Witten Diagrams for Torus Conformal Blocks
• Geometric actions and flat space holography
• Holographic conformal blocks from interacting Wilson lines
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• Conformal blocks from Wilson lines with loop corrections
• A multipoint conformal block chain in $d$ dimensions
• Correlators in higher spin AdS_3 holography from Wilson lines with loop corrections
• Wilson Lines and Ishibashi States in AdS${}_3$/CFT${}_2$
• Renormalization of gravitational Wilson lines
• Towards Feynman rules for conformal blocks
• Scalar Blocks as Gravitational Wilson Networks
• Various semiclassical limits of torus conformal blocks
• Superconformal blocks from Wilson lines with loop corrections
• Gravitational Wilson Lines in 3D de Sitter
• Bands and gaps in Nekrasov partition function
• Eternal Higher Spin Black Holes: a Thermofield Interpretation
• Geodesic description of Heavy-Light Virasoro blocks
• Late time Wilson lines
• More on Wilson toroidal networks and torus blocks
• Wilson line networks in $p$-adic AdS/CFT
• Comments on spinning OPE blocks in AdS${}_3$/CFT${}_2$
• Semi-classical BMS-blocks from the Oscillator Construction
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• A view of the bulk from the worldline
• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks
• Wilson lines construction of ${\mathfrak{sl}}_3$ toroidal conformal blocks
• c-Recursion for multi-point superconformal blocks. NS sector
• Holographic Aspects of Even-Dimensional Topological Gravity
• Crossing, Modular Averages and $N\leftrightarrow k$ in WZW Models