Work

Vogel’s universality and the classification problem for Jacobi identities

Year: 2025

Type: article

Abstract: 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.

Source: The European Physical Journal C

DOI: 10.1140/epjc/s10052-025-14943-y

Authors: A. Morozov, A. Sleptsov

Institutions: Moscow Institute of Physics and Technology, Kurchatov Institute, Institute for Information Transmission Problems, Institute for Theoretical and Experimental Physics

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Ministry of Science and Higher Education of the Russian Federation, Foundation for the Advancement of Theoretical Physics and Mathematics, Institute for Information and Communications Technology Promotion

OpenAlex ID: W4415731045