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

Author:

Manu Mathur, Atul Rathor

Keyword:

High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat)

journal:

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date:

2023-07-11 16:00:00

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 ($\text{N}-1$) angles, are the creation \& annihilation or the shift operators for the SU(N) magnetic vortices carrying $(\text{N}-1)$ 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 $(\text{N}-1)$ electric fluxes on their loops. The new order-disorder algebra involving SU(N) Wigner D matrices is derived and discussed. The $Z_\text{N} (\in $ 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.