# The Coulomb flux tube on the lattice

## TL;DR

This paper demonstrates through lattice gauge theory simulations that the Coulomb electric field between static quarks forms an exponential flux tube, indicating confinement and the absence of long-range Coulomb dipole fields.

## Contribution

It provides numerical evidence that the Coulomb electric field in Coulomb gauge forms a flux tube, a novel insight into the structure of the color field in non-Abelian gauge theories.

## Key findings

- Coulomb electric field falls off exponentially with transverse distance.
- Existence of a color Coulomb flux tube confirmed.
- Long-range Coulomb dipole fields are absent.

## Abstract

In Coulomb gauge a longitudinal electric field is generated instantaneously with the creation of a static quark-antiquark pair. The field due to the quarks is a sum of two contributions, one from the quark and one from the antiquark, and there is no obvious reason that this sum should fall off exponentially with distance from the sources. We show here, however, from numerical simulations in pure SU(2) lattice gauge theory, that the color Coulomb electric field does in fact fall off exponentially with transverse distance away from a line joining static quark-antiquark sources, indicating the existence of a color Coulomb flux tube, and the absence of long-range Coulomb dipole fields.