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

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.