# The far field limit profile functions of two overlapped dyons

## TL;DR

This paper investigates the asymptotic behavior of overlapping dyons in Yang-Mills theory, revealing that same-type dyons resemble a single dyon at infinity, while different-type dyons do not contribute to confinement.

## Contribution

It derives new equations of motion for overlapped dyons and analyzes their profile functions, providing insights into their behavior at infinity in the context of Yang-Mills theory.

## Key findings

- Same-type dyons' profiles resemble a single dyon at infinity
- Different-type dyons produce trivial holonomy
- No contribution to confinement phase from different-type dyons

## Abstract

We study the profile functions of two overlapped dyons at infinity. We assume that the superposition of two dyons satisfies Yang-Mills (Y-M) equation and then we find new equations of motion for individual dyons which do not satisfy the original Y-M equation, anymore. By solving these new equations, we find out that the profile functions of two overlapped dyons of the same type at infinity, looks like the profile functions of one dyon. However, the superposition of two dyons of different types gives trivial holonomy and therefore no contribution in the confinement phase is observed.