# Instanton, Monopole and Confinement

## TL;DR

This paper investigates the relationship between instantons and monopoles in QCD, revealing a correlation between monopole trajectories and instanton density, and observing monopole condensation in dense topological pseudoparticle environments.

## Contribution

It demonstrates a correlation between monopole trajectories and instanton numbers and explores monopole condensation in a multi-instanton vacuum using lattice gauge theory.

## Key findings

- Linear correlation between monopole trajectory length and instanton count.
- Monopole condensation indicated by clustering in dense pseudoparticle environments.
- Evidence of monopole behavior in the multi-instanton vacuum.

## Abstract

We study the correlation between instantons and QCD-monopoles both in the lattice gauge theory and in the multi-instanton system using the maximally abelian gauge. First, we find the existence of an almost linear correlation between the total length of monopole trajectories and the total number of pseudoparticles (instantons and anti-instantons) in the $16^{3}\times4$ SU(2) lattice. Second, we study the features of QCD-monopole in the SU(2) multi-instanton vacuum on the $16^{4}$ lattice as a random ensemble of pseudoparticles. A signal of monopole condensation is found as the clustering of monopole trajectories, when the topological pseudoparticles is sufficiently dense.