Exact construction of noncommutative instantons

Abstract

We discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction of U(N) instantons in noncommutative (NC) space and prove the one-to-one correspondence between moduli spaces of the noncommutative instantons and the ADHM data, together with an origin of the instanton number for U(1). We also give a derivation of the ADHM construction from the viewpoint of the Nahm transformation of instantons on four-tori. This article is a composite version of [23] and [24].

Compactness of brane moduli and the String Lamppost Principle in d > 6

“…2 Although it never happens in known string constructions, a priori, we may also consider the case where a given brane never arises as a small instanton of a non-Abelian group. In this case, the non-commutative geometry version of the ADHM construction works for U(1) instantons in non-commutative space [19], and again yields a one-dimensional Coulomb branch.…”