Abstract
We examine universal positivity constraints on 2 → 2 scattering in 4d planar \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory with higher-derivative corrections. We present numerical evidence that the convex region of allowed Wilson coefficients (the “EFT-hedron”) flattens completely along about one-third of its dimensions when an increasing number of constraints on the spectral density from crossing-symmetry are included. Our analysis relies on the formulation of the positivity constraints as a linear optimization problem, which we implement using two numerical solvers, SDPB and CPLEX. Motivated by the flattening, we propose a novel partially resummed low-energy expansion of the 2 → 2 amplitude. As part of the analysis, we provide additional evidence in favor of the conjecture [1] that the Veneziano amplitude is the only amplitude compatible with both S-matrix bootstrap constraints and string monodromy.
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Acknowledgments
We would like to thank Jan Albert, Alan Shih-Kuan Chen, Enrico Hermann, Loki Lin, Andrew Neitzke, Leonardo Rastelli, David Poland, and Nick Geiser for useful comments and discussions. We also thank Li-Yuan Chiang, Yu-tin Huang, and He-Chen Weng for sharing the draft of their paper [27] with us. HE and JB are supported in part by DE-SC0007859. AH was supported in part by a Rackham Predoctoral Fellowship from the University of Michigan and in part by the Simons Foundation.
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Berman, J., Elvang, H. & Herderschee, A. Flattening of the EFT-hedron: supersymmetric positivity bounds and the search for string theory. J. High Energ. Phys. 2024, 21 (2024). https://doi.org/10.1007/JHEP03(2024)021
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DOI: https://doi.org/10.1007/JHEP03(2024)021