2025/06/27 by J D Berman, Henriette Elvang, Berman, Justin +3 · 7 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2506.22538
openalex publication_date 2025/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study constraints from higher-point amplitudes on 2 → 2 scattering in the context of effective field theory (EFT) using the perturbative numerical S-matrix bootstrap. Specifically, we investigate the class of weakly coupled EFTs with amplitudes that obey the hidden zero and split conditions that are known to hold both for Tr(Φ3) theory and for certain string tree amplitudes, including at 4-point the beta function. Requiring the splitting condition for the 5-point amplitude not only fixes nearly all its contact terms, but it also imposes non-linear constraints among the 4-point EFT Wilson coefficients. When included in the bootstrap, the resulting allowed region consistent with positivity is no longer convex but is restricted to a smaller non-convex region - which has a sharp corner near the string beta function! Assuming the absence of an infinite spin tower at the mass gap, the allowed region bifurcates into a trivial region (with states only above a chosen cutoff) and an island that continues to shrink around the string as more constraints are included in the bootstrap. The numerics indicate that in the absence of single-mass infinite spin towers the string beta function is the unique 4-point amplitude compatible with hidden zero and the 5-point splitting constraints. The analysis provides a prototype example for how features of higher-point amplitudes constrain the bootstrap of 4-point amplitudes.