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.

35 pages, 1 figure, minor corrections

References in corpus (5)

• BPS States in Supersymmetric Chiral Models with Higher Derivative Terms
• Classifying BPS States in Supersymmetric Gauge Theories Coupled to Higher Derivative Chiral Models
• Higher Derivative Corrections to Manifestly Supersymmetric Nonlinear Realizations
• Oxidation of self-duality to 12 dimensions and beyond
• ADHM Construction of Noncommutative Instantons

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