From Gaudin Integrable Models to $d$-dimensional Multipoint Conformal Blocks

Abstract

In this work we initiate an integrability-based approach to multipoint conformal blocks for higher dimensional conformal field theories. Our main observation is that conformal blocks for $N$-point functions may be considered as eigenfunctions of integrable Gaudin Hamiltonians. This provides us with a complete set of differential equations that can be used to evaluate multipoint blocks.

arXiv comment7 pages, 1 figure; added discussion of general dimensions and general number of points in comb channel

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Cited by in corpus (16)

• Lightcone Bootstrap at higher points
• Gaudin Models and Multipoint Conformal Blocks: General Theory
• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
• Recursion relations for 5-point conformal blocks
• Shadow Celestial Amplitude
• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Improving the five-point bootstrap
• Integrability for Feynman Integrals
• Conformal partial waves in momentum space
• Defect Conformal Blocks from Appell Functions
• Universal Spinning Casimir Equations and Their Solutions
• Conformal Blocks in Two and Four Dimensions from Oscillator Representations
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Separation of variables for higher rank integrable models: review of recent progress
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions