NoncommutativeU(1)instantons in eight dimensional Yang-Mills theory

Abstract

We study the noncommutative version of the extended ADHM construction in eight dimensional $U(1)$ Yang-Mills theory. This construction gives rise to the solutions of the BPS equations in 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.