Claude reaches a new theoretical physics milestone

An LLM-based AI working with Anthropic researchers calculated the hexagon amplitude in planar 𝒩 = 4 super Yang-Mills to nine loops, exceeding the loop order humans had previously reached. The result matters because higher-loop quantum field theory calculations can sharpen predictions for quantities such as scattering amplitudes and cross-sections, which are central to comparing theory with particle physics experiments.

Matt von Hippel had challenged LLM-based systems to move beyond current limits in 𝒩 = 8 supergravity or 𝒩 = 4 super Yang-Mills. Liam Fitzpatrick and Siddharth Mishra-Sharma used Fable 5.1 within Claude Science, giving the model a brief initial prompt and only minimal follow-up direction. Claude produced the answer through both bootstrap and form-factor approaches, and Lance Dixon verified it.

The achievement remains limited: it used a toy model, relied heavily on existing work, introduced no new techniques and offered no fundamentally new physics insight. Still, the computation was considered fragile and difficult to reproduce directly, and Dixon said Claude had to build code from scratch for details not fully documented in publications.