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

## TL;DR

This paper generalizes the ADHM construction to generate (anti-)self-dual instantons in higher dimensions, specifically in 4n dimensions, and explores multi-instanton solutions and calorons within this framework.

## Contribution

The paper introduces a higher-dimensional ADHM construction for (anti-)self-dual instantons in 4n dimensions, extending known four-dimensional methods.

## Key findings

- Reproduces known 4n-dimensional one-instantons.
- Finds multi-instanton solutions of 't Hooft type.
- Discusses caloron solutions and monopole limits 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.