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

TL;DR

This paper constructs a comprehensive set of disorder operators for SU(N) lattice gauge theory in 2+1 dimensions, revealing their algebraic relations and connections to magnetic vortices and Wilson loops.

Contribution

It introduces the most general disorder operators for SU(N) lattice gauge theory, characterized by multiple magnetic flux types, and explores their algebraic structure and relation to known operators.

Findings

Constructed disorder operators for SU(N) gauge theory in 2+1D.

Derived the order-disorder algebra involving SU(N) Wigner D matrices.

Connected the new operators to the Z_N 't Hooft operator and standard Wilson-'t Hooft algebra.

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.