Poisson brackets and coaction maps of regularized holonomies of the KZ equation

Anton Alekseev, Florian Naef, Muze Ren

13/9/24 Published in : arXiv:2409.08894

We derive explicit closed formulas for the Kirillov-Kostant-Souriau (KKS) coaction maps of open path regularized holonomies of the Knizhnik-Zamolodchikov (KZ) equation, and the corresponding Poisson brackets for the Lie algebra {\rm gl}(N, \mathbb{C}). Our main technical tool is a certain projection of the generalized pentagon equation of \cite{AFR2024}.

Entire article

Phase I & II research project(s)

Field Theory
Geometry, Topology and Physics

Phase III direction(s)

Spectral gap problems in non-perturbative quantum theory
Holography and bulk-boundary correspondence
From Field Theory to Geometry and Topology

A tour d'horizon of de Casteljau's work

Equidistribution of continuous low-lying pairs of horocycles via Ratner