Aspects of $C_3$-symmetric calorons from numerical Nahm transform

TL;DR

This paper numerically investigates $C_3$-symmetric calorons using the Nahm transform, revealing how their action density diminishes as the circle's circumference approaches zero, especially for calorons without monopole limits.

Contribution

It introduces a numerical approach to analyze $C_3$-symmetric calorons via the Nahm transform, focusing on cases lacking monopole limits and their behavior as $S^1$ shrinks.

Findings

Action density fades as $S^1$ shrinks.

Zero-circumference limit can be traced for these calorons.

Calorons without monopole limits behave differently from those with limits.

Abstract

Calorons are finite action solutions to the anti-selfdual Yang-Mills equations on $\mathbb{R}^3\times S^1$. They are generally constructed by the so called Nahm construction. We perform the numerical Nahm transform for the Nahm data of 3-calorons with $C_3$-symmetry, which do not have the monopole limits. Dissimilar to the cases of having monopole limits, we can trace the zero-circumference limit of $S^1$.It is found that the action density of the calorons tends to fade away as $S^1$ shrinks.