Noncommutative Moduli for Multi-Instantons

TL;DR

This paper introduces a method to construct explicit multi-instanton solutions on noncommutative R^4 by allowing the instanton moduli to be noncommutative, enabling the ADHM construction of self-dual solutions.

Contribution

It extends the ADHM construction to noncommutative spaces by making the moduli noncommutative, facilitating explicit multi-instanton solutions with higher topological charge.

Findings

Constructed explicit 't Hooft multi-instanton solutions on noncommutative R^4.

Demonstrated self-duality of the field strengths in these solutions.

Provided a recursive algorithm for multi-instantons in the noncommutative setting.

Abstract

There exists a recursive algorithm for constructing BPST-type multi-instantons on commutative R^4. When deformed noncommutatively, however, it becomes difficult to write down non-singular instanton configurations with topological charge greater than one in explicit form. We circumvent this difficulty by allowing for the translational instanton moduli to become noncommutative as well. This makes possible the ADHM construction of 't Hooft multi-instanton solutions with everywhere self-dual field strengths on noncommutative R^4.