Collinear Gluons from Gravity: Poincaré-Birkhoff-Witt Decomposition and Twisted Intersections
Abstract
We give an explicit reconstruction of subleading collinear Yang--Mills amplitudes from one-graviton amplitudes in Einstein--Yang--Mills theory and its string corrections. We realize the monodromy kernel in the mixed open-closed string relation as a weighted Lie-algebraic recursion on words of gluon labels. At order α'r, its output contains at most r Lie factors. The Poincaré--Birkhoff--Witt (PBW) theorem decomposes the space spanned by gluon orderings into sectors whose dimensions are given by unsigned Stirling numbers of the first kind. Appropriate shuffle sums of one-graviton amplitudes extract the degree-r sector, for which the string-period matrix drops out. Accordingly, we show that the reconstruction coefficients factor into linear kinematic factors over the product of bipartition factors. Finally, we express the reconstruction coefficients as twisted intersection numbers between Parke--Taylor forms and explicit forest cocycles constructed recursively from logarithmic four-point differentials.
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BibTeX
@misc{dong2026collinear,
title = {{Collinear Gluons from Gravity: Poincaré-Birkhoff-Witt Decomposition and Twisted Intersections}},
author = {Jin Dong and Stephan Stieberger},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30235},
eprint = {2610.30235},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30235},
}
RIS
TY - UNPB
TI - Collinear Gluons from Gravity: Poincaré-Birkhoff-Witt Decomposition and Twisted Intersections
AU - Jin Dong
AU - Stephan Stieberger
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30235
UR - https://arxiv.org/abs/2610.30235
AB - We give an explicit reconstruction of subleading collinear Yang--Mills amplitudes from one-graviton amplitudes in Einstein--Yang--Mills theory and its string corrections. We realize the monodromy kernel in the mixed open-closed string relation as a weighted Lie-algebraic recursion on words of gluon labels. At order α'^r, its output contains at most r Lie factors. The Poincaré--Birkhoff--Witt (PBW) theorem decomposes the space spanned by gluon orderings into sectors whose dimensions are given by unsigned Stirling numbers of the first kind. Appropriate shuffle sums of one-graviton amplitudes extract the degree-r sector, for which the string-period matrix drops out. Accordingly, we show that the reconstruction coefficients factor into linear kinematic factors over the product of bipartition factors. Finally, we express the reconstruction coefficients as twisted intersection numbers between Parke--Taylor forms and explicit forest cocycles constructed recursively from logarithmic four-point differentials.
ER -