Abstract
Recently we showed how, in two-dimensional scalar theories, one-loop threshold diagrams can be cut into the product of one or more tree-level diagrams [1]. Using this method on the ADE series of Toda models, we computed the double- and single-pole coefficients of the Laurent expansion of the S-matrix around a pole of arbitrary even order, finding agreement with the bootstrapped results. Here we generalise the cut method explained in [1] to multiple loops and use it to simplify large networks of singular diagrams. We observe that only a small number of cut diagrams survive and contribute to the expected bootstrapped result, while most of them cancel each other out through a mechanism inherited from the tree-level integrability of these models. The simplification mechanism between cut diagrams inside networks is reminiscent of Gauss’s theorem in the space of Feynman diagrams.
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Acknowledgments
We thank Gabriele Dian, Ben Hoare and Charles Young for related discussions. This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 764850 “SAGEX”, and from the STFC under consolidated grant ST/T000708/1 “Particles, Fields and Spacetime”. It was also supported in part by the National Science Foundation under Grant No. NSF PHY-1748958 and by STARS@UNIPD, under project “Exact-Holography”.
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Dorey, P., Polvara, D. From tree- to loop-simplicity in affine Toda theories II: higher-order poles and cut decompositions. J. High Energ. Phys. 2023, 177 (2023). https://doi.org/10.1007/JHEP10(2023)177
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DOI: https://doi.org/10.1007/JHEP10(2023)177