Abstract:
I will study planar, maximally supersymmetric 4d EFTs that reduce to \mathcal{N}=4 SYM at low energies and show that novel constraints arise from the six-point amplitude. By constructing the six-scalar amplitude and imposing supersymmetry together with standard tree-level factorization, assuming parity-even scalar contact terms, I find striking nonlinear relations among the four-point Wilson coefficients. These relations collapse much of the naive EFT parameter space. When combined with positivity bounds from unitarity and causality, the allowed region in Wilson-coefficient space shrinks to a thin sliver converging on the open-superstring Veneziano amplitude, strongly suggesting that maximal supersymmetry singles out the tree-level string answer. More broadly, the result shows that higher-point amplitudes contain qualitatively new bounds on the space of EFTs, and that the space of consistent quantum field theories may be much smaller than current four-point analyses suggest.