# Scattering Amplitudes

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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 Oct 1, 2026
Schwartz used BootLoops to have Claude compute 30 Feynman integrals end to end, 15 of them never computed before
In a guest post, theoretical physicist Matthew Schwartz describes building BootLoops, an open-source harness for exact calculations in quantitative science: rather than asking Claude to work like a human scientist, he looked for "Claude-shaped" problems, and Claude reproduced in about 20 minutes results whose code took him weeks to write, completed 30 Feynman integrals end to end (15 reproductions of known results by the new method and 15 never computed before), then carried the same class of integral methods into ecology and population genetics, advancing 36 manuscripts across 18 fields with 19 coauthors in three months.
In a guest post, theoretical physicist Matthew Schwartz describes building BootLoops, an open-source harness for exact calculations in quantitative science: rather than asking Claude to work like a human scientist, he looked for "Claude-shaped" problems, and Claude reproduced in about 20 minutes results whose code took him weeks to write, completed 30 Feynman integrals end to end (15 reproductions of known results by the new method and 15 never computed before), then carried the same class of integral methods into ecology and population genetics, advancing 36 manuscripts across 18 fields with 19 coauthors in three months.
BootLoops Agentic AI Scattering Amplitudes S-matrix bootstrap Neutral biodiversity theory
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

You’re all caught up

Mass parameters move into the geometry: deformed Amplituhedron fixes the double-box span and the two-loop walking dimension

Schwartz used BootLoops to have Claude compute 30 Feynman integrals end to end, 15 of them never computed before

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