A Compact Expression for Periodic Instantons

TL;DR

This paper derives a simple, explicit formula for periodic instantons that simplifies the ADHM-Nahm construction, making calculations more straightforward and adaptable to other spaces.

Contribution

The authors present a new compact formula for periodic instantons that streamlines the ADHM-Nahm transform process and can be extended to different geometric settings.

Findings

Derived a simple explicit formula for periodic instantons

Simplified the ADHM-Nahm construction process

Potential for generalization to other spaces

Abstract

Instantons on various spaces can be constructed via a generalization of the Fourier transform called the ADHM-Nahm transform. An explicit use of this construction, however, involves rather tedious calculations. Here we derive a simple formula for instantons on a space with one periodic direction. It simplifies the ADHM-Nahm machinery and can be generalized to other spaces.