https://doi.org/10.1140/epjc/s10052-025-14943-y
Regular Article - Theoretical Physics
Vogel’s universality and the classification problem for Jacobi identities
1
Moscow Institute of Physics and Technology, 141700, Dolgoprudny, Russia
2
Institute for Information Transmission Problems, 127051, Moscow, Russia
3
NRC “Kurchatov Institute”, 123182, Moscow, Russia
4
Former Institute for Theoretical and Experimental Physics, 117218, Moscow, Russia
Received:
8
August
2025
Accepted:
13
October
2025
Published online:
31
October
2025
This paper is a summary of discussions at the recent ITEP-JINR-YerPhI workshop on Vogel theory in Dubna. We consider relation between Vogel divisor(s) and the old Dynkin classification of simple Lie algebras. We consider application to knot theory and the hidden role of Jacobi identities in the definition/invariance of Kontsevich integral, which is the knot polynomial with the values in diagrams, capable of revealing all Vassiliev invariants – including the ones, not visible in other approaches. Finally we comment on the possible breakdown of Vogel universality after the Jack/Macdonald deformation. Generalizations to affine, Yangian and DIM algebras are also mentioned. Especially interesting could be the search for universality in ordinary Yang–Mills theory and its interference with confinement phenomena.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
