Manifest supersymmetry and the ADHM construction of instantons

TL;DR

This paper develops a superspace formulation of the ADHM instanton construction using harmonic superspace, revealing a direct link between the ADHM method and twistor theory within a supersymmetric framework.

Contribution

It introduces a (0,4) superspace approach to ADHM instantons, highlighting the interplay with twistor theory and expanding the geometric understanding of instanton solutions.

Findings

Superspace formulation makes the ADHM construction manifestly supersymmetric.

Harmonic superspace formalism captures the complex structures of self-dual Yang-Mills.

The approach elucidates the connection between ADHM data and twistor space.

Abstract

We present the (0,4) superspace version of Witten's sigma model construction for ADHM instantons. We use the harmonic superspace formalism, which exploits the three complex structures common to both (0,4) supersymmetry and self-dual Yang-Mills theory. A novel feature of the superspace formulation is the manifest interplay between the ADHM construction and its twistor counterpart.