String Amplitudes on Integer Rectangles
Abstract
Hidden zeros of tree-level string amplitudes of colored scalars lie on loci specified by integer-valued dimensionless momentum contractions arranged in rectangles on the kinematic mesh. We study the same kinematic loci for open-string amplitudes with gluons, fermions and higher-spin states at arbitrary finite mass levels. Disk monodromy relations yield zero−locus factorization: at regular points where the monodromy system is invertible, the amplitude is a weighted sum of physical three-point amplitudes sewn to complete on-shell (n−1)-point amplitudes. Hidden zeros follow when the external wavefunctions annihilate all contributing three-point couplings. In the low-energy limit, the massless zero-integer branch recovers the corresponding field-theory factorization. For closed strings, including gravitons, persistent cubic zeros in both chiral sectors remove the disk poles, allowing the Kawai--Lewellen--Tye momentum-kernel zero to imply amplitude zeros. The operator product expansions of external vertices give a common worldsheet origin for these conditions across spins and mass levels.
Related
- Bosonic String Amplitudes From Ribbon Graphs
- General Form Factors from String Amplitudes
- Scattering Equations as the lowest order K-identities in the calculation of Stringy Scaling of Hard String Scattering Amplitudes
- Instanton-induced closed-string amplitudes in minimal superstring theory at subleading order
- Infrared Consistency and the Uniqueness of String Amplitudes
BibTeX
@misc{he2026string,
title = {{String Amplitudes on Integer Rectangles}},
author = {Song He and Yong Zhang and Fan Zhu and Pengfei Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31197},
eprint = {2610.31197},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31197},
}
RIS
TY - UNPB
TI - String Amplitudes on Integer Rectangles
AU - Song He
AU - Yong Zhang
AU - Fan Zhu
AU - Pengfei Zhu
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31197
UR - https://arxiv.org/abs/2610.31197
AB - Hidden zeros of tree-level string amplitudes of colored scalars lie on loci specified by integer-valued dimensionless momentum contractions arranged in rectangles on the kinematic mesh. We study the same kinematic loci for open-string amplitudes with gluons, fermions and higher-spin states at arbitrary finite mass levels. Disk monodromy relations yield zero−locus factorization: at regular points where the monodromy system is invertible, the amplitude is a weighted sum of physical three-point amplitudes sewn to complete on-shell (n−1)-point amplitudes. Hidden zeros follow when the external wavefunctions annihilate all contributing three-point couplings. In the low-energy limit, the massless zero-integer branch recovers the corresponding field-theory factorization. For closed strings, including gravitons, persistent cubic zeros in both chiral sectors remove the disk poles, allowing the Kawai--Lewellen--Tye momentum-kernel zero to imply amplitude zeros. The operator product expansions of external vertices give a common worldsheet origin for these conditions across spins and mass levels.
ER -