Continuum Gauge Fields from Lattice Gauge Fields

TL;DR

This paper develops a method to construct continuum gauge fields from lattice gauge fields, preserving gauge covariance and topological features, demonstrated explicitly in two-dimensional U(1) theory.

Contribution

It introduces a gauge covariant construction of continuum gauge fields from lattice fields, bridging the gap between lattice and continuum formulations.

Findings

Constructed continuum gauge fields from lattice fields in a gauge covariant manner.

Preserved topological charge and geometrical features in the continuum limit.

Explicitly applied the method to 2D U(1) lattice gauge theory with simple results.

Abstract

On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant and complies with geometrical constructions of the topological charge on the lattice, is given in this paper. The procedure is explicitly carried out in the $U(1)$ theory in two dimensions, where it leads to simple results.