String Theory from Maximal Supersymmetry

Abstract

We explore the space of non-gravitational, maximally supersymmetric, planar 4d effective field theories (EFTs) that have $\mathcal{N}=4$ super Yang-Mills (SYM) at leading order. In the weakly-coupled regime, we examine the combined constraints of $\mathcal{N}=4$ supersymmetry and $SU(4)$ R-symmetry together with the requirement of standard tree-level factorization on the massless poles of the 4-, 5-, and 6-point EFT scattering amplitudes. When imposing a parity condition on the 6-scalar amplitudes, we find highly nontrivial nonlinear constraints on the 4-point Wilson coefficients. When these novel constraints are combined with positivity, the resulting bounds on the 4-point Wilson coefficients converge to the values of the open string Veneziano amplitude. Our results strongly suggest that supersymmetry, R-symmetry, the parity requirement on the 6-scalar amplitudes, and positivity are sufficient to single out this unique UV completion at tree level. Our findings, moreover, highlight the power of higher-point amplitudes in constraining EFT data and imply that the space of consistent quantum field theories is even more restricted than previously suggested by causality or swampland-based approaches.

v1: 39 pages, 3 figures. v2: Important discussion and corrections included regarding local contact terms in the 6-scalar EFT amplitude. v3: Updated arXiv abstract to match the paper