Complexified moduli of non-commutative instantons

TL;DR

This paper revisits the ADHM construction for non-commutative instantons, revealing a new geometric interpretation of the size modulus through quaternionic formalism and self-dual parameters.

Contribution

It introduces a quaternionic formalism to analyze non-commutative instantons, linking the self-dual part of the non-commutativity parameter to the instanton size modulus.

Findings

Identifies the self-dual part of theta^mn as the imaginary part of the instanton size modulus.

Provides a quaternionic framework for understanding non-commutative instantons.

Reveals geometric interpretation of moduli in non-commutative gauge theories.

Abstract

We revisit the generalised ADHM construction for instantons in non-commutative space using a manifestly quaternionic formalism. This leads to an identification of the self-dual part of theta^mn as the imaginary part of the size modulus of the instanton.