Disorder operators and magnetic vortices in SU(N) lattice gauge theory

2023/07/12 by Manu Raj Mathur, Mathur, Manu, Atul Rathor +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.2307.06278

openalex publication_date 2023/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct the most general disorder operator for SU(N) lattice gauge theory in (2+1) dimension by using exact duality transformations. These disorder operators, defined on the plaquettes and characterized by (N-1) angles, are the creation & annihilation or the shift operators for the SU(N) magnetic vortices carrying (N-1) types of magnetic fluxes. They are dual to the SU(N) Wilson loop order operators which, on the other hand, are the creation-annihilation or shift operators for the (N-1) electric fluxes on their loops. The new order-disorder algebra involving SU(N) Wigner D matrices is derived and discussed. The Z_N (∈ SU(N)) 't Hooft operator is obtained as a special limit. In this limit we also recover the standard Wilson-'t Hooft order-disorder algebra. The partition function representation and the free energies of these SU(N) magnetic vortices are discussed.

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• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory, II: Operator representation for the trivalent vertex

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