# Correlation functions between topological objects -- field theoretic versus geometric definitions

## TL;DR

This study compares geometric and field theoretic definitions of topological objects in SU(2) lattice gauge theory, analyzing their correlation functions and extracting screening masses to understand their local interactions.

## Contribution

It provides a comparative analysis of topological charge definitions and their correlation functions, revealing non-trivial local correlations and dependence on cooling procedures.

## Key findings

- Topological quantities show non-trivial local correlations.
- Correlation functions fit well to exponential decay, allowing extraction of screening masses.
- Auto-correlation functions depend on cooling, affecting topological charge measurements.

## Abstract

We analyze topological objects in pure gluonic $SU(2)$ lattice gauge theory and compute correlation functions between instantons and monopoles. Concerning the instantons we use geometric and field theoretic definitions of the topological charge. On a $12^3\times 4$ lattice it turns out that topological quantities have a non-trivial local correlation. The auto-correlation functions of the topological charge depend on cooling for both definitions. We fit the correlation functions to exponentials and obtain screening masses.