Abstract
We compute the six-particle maximally-helicity-violating (MHV) amplitude in planar \( \mathcal{N} \) = 4 super-Yang-Mills theory at eight loops, using antipodal duality and the recently computed eight-loop three-point form factor for the chiral stress energy tensor multiplet. Antipodal duality maps the form factor symbol to the amplitude symbol on a two-dimensional parity-preserving surface in the three-dimensional amplitude kinematics. There are remarkably few ambiguities in lifting from two to three dimensions, nor in promoting the symbol to a function. The amplitude passes many tests, including near-collinear, multi-Regge, factorization, self-crossing and origin limits. These checks also constitute a validation of antipodal duality at eight loops.
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Acknowledgments
We are grateful to Ömer Gürdoğan, Andrew McLeod and Matthias Wilhelm for collaboration on earlier related projects and for stimulating discussions. We also thank Benjamin Basso for useful conversations. This research was supported by the US Department of Energy under contracts DE-AC02-76SF00515 and DE-FOA-0002705, KA/OR55/22 (AI-HEP), and by the Munich Institute for Astro-, Particle and BioPhysics (MIAPbP) which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2094 – 390783311. LD thanks MIAPbP for hospitality during part of the writing of this paper.
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Dixon, L.J., Liu, YT. An eight loop amplitude via antipodal duality. J. High Energ. Phys. 2023, 98 (2023). https://doi.org/10.1007/JHEP09(2023)098
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DOI: https://doi.org/10.1007/JHEP09(2023)098