Lattice gauge theory can be used to construct many models of quantum fields that we don't know how to construct in smooth spacetime. In lattice gauge theory with gauged group G, a gauge field is described using G-valued link variables associated with the links in the lattice, or more generally with the edges in a graph. The graph is meant to be a kind of discrete approximation to a manifold M representing continuous space or spacetime. This article explains how that formulation of lattice gauge theory relates to principal G-bundles and connections on M.
