ADHM Construction of (Anti-)Self-dual Instantons in $4n$ Dimensions

Abstract

The ADHM construction is a very strong scheme to construct the instantons in four dimensions. We study an ADHM construction of instantons in $4n~(n\geq2)$ dimensions by generalizing this scheme. The higher-dimensional ADHM construction generates the $4n$-dimensional (anti-)self-dual instantons which satisfy the (anti-)self-dual equation in $4n$ dimensions: $F(n)=\pm\ast_{4n}F(n)$. Here $F(n)$ is the $n$th wedge products of the gauge field strength 2-form $F$. We also show that our scheme reproduces the known $4n$-dimensional one-instantons and there are multi-instanton solutions of the 't Hooft type in the dilute instanton gas limit. Moreover we discuss a Harrington-Shepard type caloron in $4n$ dimensions and this monopole limit.