Symmetric Calorons

TL;DR

This paper demonstrates the existence of symmetric calorons for charges up to four, linking symmetric monopoles, instantons, and Skyrmions through a continuous family of solutions.

Contribution

It introduces symmetric calorons as a new class connecting monopoles, instantons, and Skyrmions, with explicit symmetry properties for charges up to four.

Findings

Existence of symmetric calorons for N ≤ 4

Symmetric calorons interpolate between monopoles and instantons

Limit cases recover symmetric monopoles and instantons

Abstract

Calorons (periodic instantons) interpolate between monopoles and instantons, and their holonomy gives approximate Skyrmion configurations. We show that, for each caloron charge N \leq 4, there exists a one-parameter family of calorons which are symmetric under subgroups of the three-dimensional rotation group. In each family, the corresponding symmetric monopoles and symmetric instantons occur as limiting cases. Symmetric calorons therefore provide a connection between symmetric monopoles, symmetric instantons and Skyrmions.