Kink Chains from Instantons on a Torus

TL;DR

This paper extends the method of deriving soliton solutions from instanton holonomies to create kink chains on a torus, providing accurate approximations with potential relevance to Skyrme crystals.

Contribution

It introduces a new approach to construct kink chains from CP1 instantons on a torus, expanding the application of instanton holonomies to soliton crystals.

Findings

Sine-Gordon kink chains can be accurately approximated from CP1 instantons.

The method provides remarkably precise solutions to the kink chain problem.

Relevance to Skyrme crystals suggests broader applications.

Abstract

We describe how the procedure of calculating approximate solitons from instanton holonomies may be extended to the case of soliton crystals. It is shown how sine-Gordon kink chains may be obtained from CP1 instantons on a torus. These kink chains turn out to be remarkably accurate approximations to the true solutions. Some remarks on the relevance of this work to Skyrme crystals are also made.