Topological Charge of Lattice Abelian Gauge Theory

TL;DR

This paper explores the topological properties of lattice abelian gauge theories, defining a topological charge via a lattice analogue of the Chern character, linking it to the winding number of a U(1) bundle.

Contribution

It introduces a method to define a topological charge on the lattice using noncommutative differential calculus, connecting lattice gauge theory with topological invariants.

Findings

Topological charge is related to the winding number of the U(1) bundle.

A lattice analogue of the Chern character is constructed.

Configuration space becomes topologically disconnected by excising certain configurations.

Abstract

Configuration space of abelian gauge theory on a periodic lattice becomes topologically disconnected by excising exceptional gauge field configurations. It is possible to define a U(1) bundle from the nonexceptional link variables by a smooth interpolation of the transition functions. The lattice analogue of Chern character obtained by a cohomological technique based on the noncommutative differential calculus is shown to give a topological charge related to the topological winding number of the U(1) bundle.