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# N=4 Super Yang-Mills

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arXiv Oct 29, 2026
Mass parameters move into the geometry: deformed Amplituhedron fixes the double-box span and the two-loop walking dimension
Four-point amplitudes on the Coulomb branch of planar super Yang–Mills had a deformed-Amplituhedron description only for a two-parameter mass configuration. Encoding the external massive kinematics in a six-parameter embedding-space Gram matrix, and using copositivity of its inverse to decide which algebraic intersections enter the real positive region, restricts the two-loop canonical numerator to the span of the two planar double boxes. In a three-parameter subfamily the one- and two-loop integrals are given analytically in multiple polylogarithms, the infrared logarithms still exponentiate at two loops, and the two-loop walking anomalous dimension is fixed.
Four-point amplitudes on the Coulomb branch of planar super Yang–Mills had a deformed-Amplituhedron description only for a two-parameter mass configuration. Encoding the external massive kinematics in a six-parameter embedding-space Gram matrix, and using copositivity of its inverse to decide which algebraic intersections enter the real positive region, restricts the two-loop canonical numerator to the span of the two planar double boxes. In a three-parameter subfamily the one- and two-loop integrals are given analytically in multiple polylogarithms, the infrared logarithms still exponentiate at two loops, and the two-loop walking anomalous dimension is fixed.
University of Hyderabad California Institute of Technology
Francesco Calisto（First author）
Deformed Amplituhedron Scattering Amplitudes N=4 Super Yang-Mills Walking Anomalous Dimension Finite Differential Equations
Anthropic Sep 25, 2026
Von Hippel's nine-loop bounty: Anthropic's Claude computed the six-particle nine-loop amplitude for about $100 of compute, and Dixon independently validated it
Physicist and science writer Matt von Hippel publicly challenged AI companies to solve a hard scattering-amplitude problem on an academic budget; Anthropic's Liam Fitzpatrick and Siddharth Mishra-Sharma used Fable 5.1 inside the Claude Science platform, gave Claude a single problem statement and then mostly just told it to keep going, and Claude computed the six-particle (hexagon) nine-loop amplitude in planar N=4 super Yang-Mills two different ways, via the original bootstrap and via the indirect form-factor route, with the bootstrap portion costing about $100, equivalent to running 96 CPUs for a week; Lance Dixon of SLAC then independently validated the result, and Song He's group at the Chinese Academy of Sciences had also computed the symbol piece of the nine-loop amplitude with GPT-6
Physicist and science writer Matt von Hippel publicly challenged AI companies to solve a hard scattering-amplitude problem on an academic budget; Anthropic's Liam Fitzpatrick and Siddharth Mishra-Sharma used Fable 5.1 inside the Claude Science platform, gave Claude a single problem statement and then mostly just told it to keep going, and Claude computed the six-particle (hexagon) nine-loop amplitude in planar N=4 super Yang-Mills two different ways, via the original bootstrap and via the indirect form-factor route, with the bootstrap portion costing about $100, equivalent to running 96 CPUs for a week; Lance Dixon of SLAC then independently validated the result, and Song He's group at the Chinese Academy of Sciences had also computed the symbol piece of the nine-loop amplitude with GPT-6
Anthropic
Claude Science Claude N=4 Super Yang-Mills Scattering Amplitudes AI-computed nine-loop amplitude in planar N=4 SYM

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