English

Motivic coaction and single-valued map of polylogarithms from zeta generators

High Energy Physics - Theory 2024-09-17 v2 Algebraic Geometry Number Theory

Abstract

We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. In both cases, the appearance of multiple zeta values is controlled by conjugating generating series of polylogarithms with Lie-algebra generators associated with odd zeta values. Our reformulation of earlier constructions of coactions and single-valued polylogarithms preserves choices of fibration bases, exposes the correlation between multiple zeta values of different depths and paves the way for generalizations beyond genus zero.

Keywords

Cite

@article{arxiv.2312.00697,
  title  = {Motivic coaction and single-valued map of polylogarithms 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:2312.00697},
  year   = {2024}
}

Comments

13 pages; v2: minor corrections and clarifications; matches published version