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arXiv · 2609.25025

String-Monodromy Rigidity from Six-Point Consistency

Jianqi Sheng
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Abstract

Can the characteristic monodromy of string scattering be derived from S-matrix consistency alone, without assuming a worldsheet? We show that finite-particle consistency fixes it to a sharply defined extent. In a massless doubly ordered identity model, two exact six-point residues generate a scalar pentagon and the odd Fay identity, forcing every analytic four-point null kernel to satisfy $q''=κq$ and leaving only the linear, trigonometric, and hyperbolic branches. This converts finite-multiplicity factorization into an all-orders constraint normally associated with worldsheet geometry. For a crossing-symmetric target in the opposite KLT module, positive unsubtracted dispersion with nonzero heavy spectral weight selects the trigonometric branch, and moment determinacy fixes the Veneziano germ up to scale. A two-scale counterexample proves that module entrance is an independent input. Our result therefore identifies both a finite-to-infinite rigidity mechanism for string scattering and the precise missing principle needed for a first-principles derivation.

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Jianqi Sheng. 2026-08-14. String-Monodromy Rigidity from Six-Point Consistency. https://arxiv.org/abs/2609.25025

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