String-Monodromy Rigidity from Six-Point Consistency
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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BibTeX
@misc{sheng2026stringmonodromy,
title = {{String-Monodromy Rigidity from Six-Point Consistency}},
author = {Jianqi Sheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25025},
eprint = {2609.25025},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25025},
}
RIS
TY - UNPB
TI - String-Monodromy Rigidity from Six-Point Consistency
AU - Jianqi Sheng
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.25025
UR - https://arxiv.org/abs/2609.25025
AB - 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.
ER -