Abstract
We propose a dual Wilson loop description for the MHV super form factors of half-BPS operators in planar \( \mathcal{N} \) = 4 super-Yang-Mills theory. In this description, the local operators are represented by on-shell states, made out of zero-momentum particles, that are absorbed by a null periodic super Wilson loop. We present evidence for this duality at weak coupling, by performing an explicit calculation of the Wilson loop matrix elements through one loop. At tree level, the interactions localize at the cusps of the loop, revealing a simple connection between the super form factors and the m = 2 tree amplituhedron. At loop level, we show that the Wilson loop calculation reproduces the known results for the super form factors. Inspired by this duality, we extend the OPE program developed for the form factors of the Lagrangian to the super form factors of the higher-charge operators. We introduce non-perturbative axioms and conjectures for the main building blocks that govern the exchange of the lightest flux-tube excitations. These blocks appear as simple refinements of the form factor transitions introduced in earlier OPE studies. They are expressed at any value of the ’t Hooft coupling in terms of the tilted Beisert-Eden-Staudacher kernel. We carry out checks of our conjectures up to two loops at weak coupling for three- and four-point form factors of half-BPS operators of various lengths, finding perfect agreement with perturbative data.
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Acknowledgments
It is a pleasure to thank Lance Dixon, Lionel Mason, Amit Sever and Matthias Wilhelm for inspiring discussions and comments on the manuscript. We are also grateful to Amit Sever for several clarifications on periodic Wilson loops and to Lance Dixon for collaboration on a related project. AT was supported by the Institut Philippe Meyer at the Ecole Normale Supérieure in Paris.
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Basso, B., Tumanov, A.G. Wilson loop duality and OPE for super form factors of half-BPS operators. J. High Energ. Phys. 2024, 22 (2024). https://doi.org/10.1007/JHEP02(2024)022
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DOI: https://doi.org/10.1007/JHEP02(2024)022