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

TL;DR

This paper develops an exact duality transformation for SU(N) lattice gauge theory in (2+1) dimensions, transforming the original gauge variables into magnetic flux loops and scalar potentials, revealing new insights into the theory's local dynamics.

Contribution

The authors construct an exact duality in SU(N) lattice gauge theory using iterative canonical transformations, enabling a local description of flux loops and scalar potentials, and generalizing to higher dimensions.

Findings

Duality maps gauge fields to magnetic flux loops and scalar potentials.

Nonlocal loop interactions can be made local with auxiliary gauge fields.

The methods are extendable to (3+1) dimensions.

Abstract

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