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 a general scheme to construct the (anti-)self-dual gauge field configurations F∧F=±⁎8F∧F whose finite topological charges are given by the fourth Chern number. We show that our construction reproduces the known SO(8) one-instanton solution. We also construct multi-instanton solutions of the 't Hooft and the 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,…) dimensions.