Self-dual Yang-Mills Equations in Split Signature

TL;DR

This paper explores the self-dual Yang-Mills equations in split signature, introducing a basic instanton solution, adapting the ADHM construction, and developing a split t'Hooft ansatz.

Contribution

It presents the first detailed analysis of self-dual Yang-Mills equations in split signature, including a new basic instanton, split ADHM construction, and split t'Hooft ansatz.

Findings

Introduction of the basic split instanton solution

Development of a split version of the ADHM construction

Description of a split t'Hooft ansatz

Abstract

We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.