Exact duality and local dynamics in SU(N) lattice gauge theory

We construct exact duality transformations in pure SU(N) Hamiltonian lattice gauge theory ($2+1$) dimension. This is obtained by making a series of iterative canonical on the electric vector fields and their conjugate magnetic potentials four links around every plaquette. The resulting dual description terms scalar or plaquette flux loops potentials. Under they both transform like adjoint matter fields. describes nonlocal self-interactions these with inverted coupling. show that loop interactions can be made local converted into minimal couplings introducing auxiliary along new constraints. included through techniques easily generalized to ($3+1$) dimensions.