Claude computes a nine-loop scattering amplitude

Two Anthropic physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, used Fable 5.1 inside Claude Science to compute the nine-loop MHV six-particle amplitude in planar N=4 super Yang-Mills, a scattering amplitude calculation that had never been done. The result was independently validated by Lance Dixon at SLAC, and the full data is published. The bootstrap route cost about $100 in compute, roughly 96 CPUs for a week.

What’s actually new

• The prompt was one line. After asking Claude which problem it was most likely to tackle, the team gave it “compute the six-particle hexagon amplitude in planar N=4 SYM at nine loops,” then told it to keep working unattended with updates every four to six hours. It completed the calculation without outside collaboration.
• Two independent methods, agreed. Claude ran the original bootstrap approach and the indirect form-factor approach Dixon had used to reach eight loops. Dixon notes the amplitude route was the impressive part, since his own group expected nine loops to be reachable only indirectly, and the setup is so fragile that any mistake collapses the whole recipe.
• A budget, not a cluster. The bootstrap leg ran in Python with SymPy for about $100. Either full approach would have cost an end user roughly $1,000 to $2,000, mostly because Claude was left running for so long.
• Humans were scooped within two weeks. Song He’s group at the Chinese Academy of Sciences had already reached most of the result using GPT-6 for constraint work, though not the overall framework. Dixon had been working toward the nine-loop form factor for a couple of years.

Why it matters

Worth reading the author’s honest conclusion rather than the headline: Claude did not invent a new method. It executed a recipe that human researchers had developed over years, with somewhat more compute than people had been willing to spend, and did it in one pass. Dixon says the result is presented in the exact format his group already used, and that Claude now understands their 2019 and 2023 papers better than anyone outside their co-authors. His real caution is about what comes next, when models start producing new physical principles rather than faithfully running known methods.

For calibration, most scattering amplitudes have only ever been calculated to two loops, a few to three, and the most precise prediction in particle physics used five. The authors both argue the real takeaway is how much low-hanging fruit remains in fields with small expert communities, and they are careful to note that real-world amplitudes are a wider, more contested frontier.

(Original source: Anthropic)