# Analytical and Numerical Study of the Aharonov--Bohm Effect in 3D and 4D Abelian Higgs Model

## TL;DR

This paper investigates the Aharonov--Bohm effect in 3D and 4D Abelian Higgs models, demonstrating its role in long-range interactions and confinement through analytical and numerical methods.

## Contribution

It provides the first analytical demonstration of the Aharonov--Bohm effect causing confinement in 3D Abelian Higgs models and confirms this effect numerically.

## Key findings

- Aharonov--Bohm effect induces long-range Coulomb interactions.
- The effect leads to confinement in three dimensions.
- Numerical evidence supports the analytical results.

## Abstract

We discuss the Aharonov--Bohm effect in three and four dimensional non--compact lattice Abelian Higgs model. We show analytically that this effect leads to the long--range Coulomb interaction of the charged particles, which is confining in three dimensions. The Aharonov--Bohm effect is found in numerical calculations in 3D Abelian Higgs model.