# Distribution of Instanton and Monopole Clustering

## TL;DR

This study investigates how instanton density affects monopole loop formation in SU(2) gauge theory, revealing that dense instanton configurations lead to long monopole loops associated with confinement.

## Contribution

It provides the first detailed analysis of the relationship between instanton distribution and monopole clustering in lattice gauge theory with abelian gauge fixing.

## Key findings

- Dilute instanton density results in small monopole loops.
- Dense instanton density leads to a single long monopole loop per configuration.
- Long monopole loops are linked to the confinement property.

## Abstract

We study the relation between the instanton distribution and the monopole loop length in the SU(2) gauge theory with the abelian gauge fixing. We measure the monopole current from the multi-instanton ensemble on the $16^4$ lattice using the maximally abelian gauge. When the instanton density is dilute, there appear only small monopole loops. On the other hand, in the dense case, there appears one very long monopole loop, which is responsible for the confinement property, in each gauge configuration. We find a clear monopole clustering in the histogram of the monopole loop length from 240 gauge configurations.