A lattice discretization of abelian gauge theories

Abelian gauge theories on the lattice: $θ$-terms and compact gauge theory with(out) monopoles

We discuss a particular lattice discretization of abelian gauge theories in arbitrary dimensions, which results in a villain type action.We show that this construction has several benefits over the conventional lattice gauge theory construction, such as electric-magnetic duality, natural coupling of the theory to magnetically charged matter in fourdimensions, complete control over the monopoles and their charges in threedimensions and a natural in two dimensions.For bosonic matter our formulation can be mapped to a worldline/worldsheet representation where the complex action problem is solved.We illustrate our construction by explicit dualizations of the and the gauge higgs model in with a term, as well as the gauge higgs model in with constrained monopole charges.