# Correlation functions between monopoles and instantons

## TL;DR

This paper investigates the relationship between monopoles and instantons in pure QCD by analyzing local correlation functions, revealing a spatial correlation of about two lattice spacings that remains stable under cooling.

## Contribution

It provides the first detailed analysis of monopole-instanton correlations in both phases of pure QCD using lattice calculations.

## Key findings

- Topological charge densities correlate with monopole densities within two lattice spacings.
- Monopole-instanton correlations are stable under gauge field cooling.
- Correlation length is approximately two lattice spacings.

## Abstract

We analyze the relation between instantons and abelian projected monopoles in both phases of pure QCD by calculating local correlation functions between topological charge densities and monopole densities. On an $8^{3} \times 4$ lattice, it turns out that topological quantities are correlated approximately two lattice spacings. The monopole-instanton correlations are rather insensitive under cooling of gauge fields.

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Source: https://tomesphere.com/paper/hep-lat/9510024