Noncommutative U(1) Instantons in Eight Dimensional Yang-Mills Theory

TL;DR

This paper explores noncommutative U(1) instantons in eight-dimensional Yang-Mills theory, revealing their supersymmetry properties, topological charges, and interpretations as D-brane charges in string theory.

Contribution

It extends the ADHM construction to eight dimensions, clarifies the interpretation of the integer parameter as D-brane charge, and relates solutions to generating techniques in noncommutative gauge theory.

Findings

The solutions preserve at least 3/16 supersymmetry.

The integer k corresponds to D4-brane charge in anti-self-dual case.

The integer k corresponds to D0-brane charge bound to D8-brane in self-dual case.

Abstract

We study the noncommutative version of the extended ADHM construction in the eight dimensional U(1) Yang-Mills theory. This construction gives rise to the solutions of the BPS equations in the Yang-Mills theory, and these solutions preserve at least 3/16 of supersymmetries. In a wide subspace of the extended ADHM data, we show that the integer $k$ which appears in the extended ADHM construction should be interpreted as the $D4$-brane charge rather than the $D0$-brane charge by explicitly calculating the topological charges in the case that the noncommutativity parameter is anti-self-dual. We also find the relationship with the solution generating technique and show that the integer $k$ can be interpreted as the charge of the $D0$-brane bound to the $D8$-brane with the $B$-field in the case that the noncommutativity parameter is self-dual.