Abstract
We argue that the Sklyanin Poisson bracket on Gr(4, n) can be used to efficiently test whether an amplitude in planar \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory satisfies cluster adjacency. We use this test to show that cluster adjacency is satisfied by all one- and two-loop MHV amplitudes in this theory, once suitably regulated. Using this technique we also demonstrate that cluster adjacency implies the extended Steinmann relations at all particle multiplicities.
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Golden, J., McLeod, A.J., Spradlin, M. et al. The Sklyanin bracket and cluster adjacency at all multiplicity. J. High Energ. Phys. 2019, 195 (2019). https://doi.org/10.1007/JHEP03(2019)195
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DOI: https://doi.org/10.1007/JHEP03(2019)195