Deriving motivic coactions and single-valued maps at genus zero from zeta generators
High Energy Physics - Theory
2026-04-23 v2 Algebraic Geometry
Number Theory
Abstract
Multiple polylogarithms are equipped with rich algebraic structures including the motivic coaction and the single-valued map which both found fruitful applications in high-energy physics. In recent work arXiv:2312.00697, the current authors presented a conjectural reformulation of the motivic coaction and the single-valued map via zeta generators, certain operations on non-commuting variables in suitable generating series of multiple polylogarithms. In this work, the conjectures of the reference will be proven for multiple polylogarithms that depend on any number of variables on the Riemann sphere.
Keywords
Cite
@article{arxiv.2503.02096,
title = {Deriving motivic coactions and single-valued maps at genus zero from zeta generators},
author = {Hadleigh Frost and Martijn Hidding and Deepak Kamlesh and Carlos Rodriguez and Oliver Schlotterer and Bram Verbeek},
journal= {arXiv preprint arXiv:2503.02096},
year = {2026}
}
Comments
40 + 11 pages; v2: numerous improvements throughout the file in response to referee feedback, version to be published in CNTP