String Theory from Maximal Supersymmetry

TL;DR

This paper investigates the constraints on 4d maximally supersymmetric EFTs, showing that supersymmetry, R-symmetry, and positivity uniquely determine the open string Veneziano amplitude at tree level.

Contribution

It demonstrates that combined symmetry and positivity constraints can single out the open string Veneziano amplitude as the unique UV completion at tree level.

Findings

Constraints from supersymmetry and R-symmetry are highly non-trivial.

Positivity combined with these constraints leads to bounds matching the Veneziano amplitude.

Higher-point amplitudes provide strong restrictions on EFT data.

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. We show that in the weakly-coupled regime, highly non-trivial nonlinear constraints on the 4-point Wilson coefficients follow from enforcing $\mathcal{N}=4$ 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. Additionally, 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, 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.