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

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.