Six-point consistency and uniqueness of the Veneziano amplitude
Abstract
We establish uniqueness of the Veneziano four-point amplitude in a meromorphic class by combining six-point consistency with a known low-order supersymmetry relation. We consider planar tree-level scattering in four dimensions with a massless maximally supersymmetric vector multiplet and an additional scalar parity condition. A difference of supersymmetry Ward identities isolates massless factorization residues and eliminates every permitted contribution regular in a common kinematic limit. The resulting functional equation holds at every derivative order and fixes all angular dependence from the forward function after subtraction of the massless poles, at fixed Yang-Mills coupling. For a jointly meromorphic amplitude with simple planar poles, a nonempty spectrum of positive mass-squared poles separated from zero by a mass gap, nonnegative coefficients in the partial-wave expansions of scalar residues, and an exact unsubtracted forward dispersion relation, only the pole positions remain free. Positivity bounds their separation. The low-order relation saturates a sharp spectral inequality, requiring an infinite sequence of equally spaced mass-squared poles. The coupling and first massive pole position therefore determine the complete four-point function and all residues, without an initial finite-spin restriction.
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BibTeX
@misc{sung2026sixpoint,
title = {{Six-point consistency and uniqueness of the Veneziano amplitude}},
author = {Ilmo Sung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29919},
eprint = {2609.29919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29919},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Six-point consistency and uniqueness of the Veneziano amplitude
AU - Ilmo Sung
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29919
UR - https://arxiv.org/abs/2609.29919
AB - We establish uniqueness of the Veneziano four-point amplitude in a meromorphic class by combining six-point consistency with a known low-order supersymmetry relation. We consider planar tree-level scattering in four dimensions with a massless maximally supersymmetric vector multiplet and an additional scalar parity condition. A difference of supersymmetry Ward identities isolates massless factorization residues and eliminates every permitted contribution regular in a common kinematic limit. The resulting functional equation holds at every derivative order and fixes all angular dependence from the forward function after subtraction of the massless poles, at fixed Yang-Mills coupling. For a jointly meromorphic amplitude with simple planar poles, a nonempty spectrum of positive mass-squared poles separated from zero by a mass gap, nonnegative coefficients in the partial-wave expansions of scalar residues, and an exact unsubtracted forward dispersion relation, only the pole positions remain free. Positivity bounds their separation. The low-order relation saturates a sharp spectral inequality, requiring an infinite sequence of equally spaced mass-squared poles. The coupling and first massive pole position therefore determine the complete four-point function and all residues, without an initial finite-spin restriction.
ER -