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

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arxiv 2009.11882 v2 pith:PB3EN3E6 submitted 2020-09-24 hep-th math-phmath.MP

classification hep-thmath-phmath.MP
keywords blocksconformalmultipointdimensionalgaudinintegrableapproachcomplete
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Casimir Radial Parts via Matsuki Decomposition

    math.RT 2024-12 conditional novelty 7.0 of 10

    A rigorous derivation of Casimir radial parts for non-compact symmetric pairs via Matsuki decomposition, applied to Lorentzian and defect conformal blocks.

  2. Thermal $n$-Point Conformal Blocks in Four Dimensions from Oscillator Representations

    hep-th 2025-07 conditional novelty 6.0 of 10

    New analytic formulas for four-dimensional thermal n-point conformal blocks are derived from oscillator representations, with a correct low-temperature limit to vacuum comb-channel blocks.

  3. Feynman Diagrams from Conformal Integrals

    hep-th 2024-12 conditional novelty 6.0 of 10

    Any massless-internal Feynman integral is a limit of a conformal integral, letting conformal-family computations supply exact answers for many Feynman diagrams.

  4. Lorentzian OPE Inversion Formula: A Geometric Perspective

    hep-th 2025-01 conditional novelty 5.0 of 10

    The Mellin transform of a Radon-transformed (auxiliary) four-point function reproduces the Lorentzian OPE partial wave amplitudes, giving a geometric projection-slice interpretation.

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