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.. Authors: Berman, Justin [University of Michigan, Ann Arbor, MI (United States)] (ORCID:0000000251279094); Elvang, Henriette [University of Michigan, Ann Arbor, MI (United States)] (ORCID:0000000260496779); Herderschee, Aidan [Institute for Advanced Study, Princeton, NJ (United States)] (ORCID:0000000299577998). DOE Contract: SC0007859. Subjects: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Scattering Amplitudes; Supersymmetric Effective Theories; Supersymmetric Gauge Theory