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arXiv · 2610.30235

Collinear Gluons from Gravity: Poincaré-Birkhoff-Witt Decomposition and Twisted Intersections

Jin Dong·Stephan Stieberger
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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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Jin Dong, Stephan Stieberger. 2026-10-21. Collinear Gluons from Gravity: Poincaré-Birkhoff-Witt Decomposition and Twisted Intersections. https://arxiv.org/abs/2610.30235

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