Flattening of the EFT-hedron: supersymmetric positivity bounds and the search for string theory

We examine universal positivity constraints on 2 → 2 scattering in 4d planar 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.