ADHM Construction of (Anti-)Self-dual Instantons in Eight Dimensions

TL;DR

This paper extends the ADHM construction to eight-dimensional (anti-)self-dual instantons, providing explicit solutions including multi-instantons and generalizations to higher dimensions, with accurate topological charge calculations.

Contribution

It introduces a general scheme for constructing (anti-)self-dual instantons in eight and higher dimensions, including multi-instanton solutions and reproduces known solutions.

Findings

Reproduces the known SO(8) one-instanton solution.

Constructs multi-instanton solutions of 't Hooft and JNR types.

Generalizes the construction to 4n dimensions.

Abstract

We study the ADHM construction of (anti-)self-dual instantons in eight dimensions. We propose the general scheme to construct the (anti-)self-dual gauge field configurations $F \wedge F = \pm *_8 F \wedge F$ whose finite topological charges are given by the fourth Chern number. We show that our construction reproduces the known $\text{SO}(8)$ one-instanton solution. We also construct multi-instanton solutions of 't Hooft and Jackiw-Nohl-Rebbi (JNR) types in the dilute instanton gas approximation. The well-separated configurations of multi-instantons reproduce the correct topological charges with high accuracy. We also show that our construction is generalized to (anti-)self-dual instantons in $4n \ (n=3,4, \ldots)$ dimensions.