On non-trivial spectra of trivial gauge theories

TL;DR

This paper analyzes the spectrum of a 2D U(1) gauge theory, revealing topological electric fluxes and their properties, and extends the analysis to systems with strings, charges, and the theta parameter.

Contribution

It provides an exact analytic solution for the spectrum of a trivial gauge theory, connecting it to topological fluxes and extending to systems with external charges and strings.

Findings

Revealed Manton's spectrum in the continuum limit

Extended analysis to systems with strings and external charges

Provided a new interpretation of the theta parameter

Abstract

In this Letter we point out that the analytic solution of the two dimensional U(1) gauge theory, on a finite lattice, reveals in the continuum limit the renowned Manton's spectrum of topological electric fluxes together with their effective hamiltonian and wave functions. We extend this result for the system with strings and external charges providing also a novel interpretation of the theta parameter. Some further generalizations are also outlined.