ADHM Construction of (Anti-)Self-dual Instantons in Eight 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 $F\wedge F=\pm {\ast }_{8}F\wedge F$ 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 $4n(n=3,4,\dots )$ dimensions.

arXiv comment35 pages, 1 figure, minor corrections

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• A Unified Construction of Skyrme-type Non-linear sigma Models via The Higher Dimensional Landau Models
• Spin(7) and generalized SO(8) instantons in eight dimensions
• Solitons and exotic instantons
• Exotic instantons in eight dimensions