ADHM 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].Comment: 23pages, 3 figures, LaTeX; A composite version of proceedings of the 20th International Colloquium on Integrable Systems and Quantum Symmetries (ISQS20), 17-23 June 2012, Prague, Czech Republic and the 10th International Conference on Symmetries and Integrability of Difference Equations (SIDE10), 11-15 June 2012, Ningbo, Chin