Abstract
We establish an all-loop conformal Yangian symmetry for the full set of planar amplitudes in the recently proposed integrable bi-scalar field theory in four dimensions. This chiral theory is a particular double scaling limit of γ-twisted weakly coupled \( \mathcal{N}=4 \) SYM theory. Each amplitude with a certain order of scalar particles is given by a single fishnet Feynman graph of disc topology cut out of a regular square lattice. The Yangian can be realized by the action of a product of Lax operators with a specific sequence of inhomogeneity parameters on the boundary of the disc. Based on this observation, the Yangian generators of level one for generic bi-scalar amplitudes are explicitly constructed. Finally, we comment on the relation to the dual conformal symmetry of these scattering amplitudes.
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ArXiv ePrint: 1704.01967
This paper is dedicated to the memory of L.D. Faddeev.
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Chicherin, D., Kazakov, V., Loebbert, F. et al. Yangian symmetry for bi-scalar loop amplitudes. J. High Energ. Phys. 2018, 3 (2018). https://doi.org/10.1007/JHEP05(2018)003
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DOI: https://doi.org/10.1007/JHEP05(2018)003