Nine-loop six-particle MHV amplitudes in planar N=4 super Yang–Mills
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How can the six-particle maximally helicity-violating amplitude in planar N=4 super Yang–Mills be calculated at nine loops using the established bootstrap framework?
Why it matters and what counts as progress
Why it matters: Extending an eight-loop calculation adds perturbative data at the frontier of this amplitude program.
What counts as progress: A nine-loop symbol or function satisfying the stated bootstrap constraints and independent coefficient comparisons, distinguishing modular data, certified rational reconstruction and unreconstructed coordinates.
How the problem developed
- 2019 · Loop result [1]
Simon Caron-Huot, Lance J. Dixon, Falko Dulat, Matt von Hippel, Andrew J. McLeod and Georgios Papathanasiou Bootstrapped the six-particle amplitude through six and seven loops, extending the known perturbative calculation.
- 15 Sept 2023 · Loop result [2]
Lance J. Dixon and Yu-Ting Liu Computed the six-particle MHV amplitude at eight loops using antipodal duality.
- 25 Sept 2026 · Loop result [3]
Claude; physicist Lance Dixon independently checked the reported nine-loop result Reported a direct computation of the nine-loop amplitude; the published account describes Dixon’s independent check of the result.
AI contribution
Claude computes a nine-loop six-particle amplitude
Claude computed the nine-loop six-particle MHV amplitude in planar N=4 super Yang–Mills using established bootstrap methods. The released symbol uses quintuple coproducts modulo two 31-bit primes; most, but not all, nonzero coordinates are reconstructed as certified rationals. A separate direct bootstrap agrees on compared coefficients, and a nine-loop function is reported.
Sources
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