Construction of Noncommutative Instantons in 4k Dimensions
Johannes Broedel, Tatiana A. Ivanova, Olaf Lechtenfeld
TL;DR
This paper develops a method to construct noncommutative instantons in higher dimensions using an extended ADHM approach, connecting these solutions to classical instantons in the commutative limit.
Contribution
It introduces a novel extension of the ADHM construction for noncommutative instantons in 4k dimensions, generalizing known solutions like 't Hooft and BPST instantons.
Findings
Constructed new noncommutative instanton solutions in 4k dimensions.
Demonstrated that in the commutative limit, solutions match classical instantons on HP^n.
Extended the ADHM method to higher-dimensional noncommutative gauge theories.
Abstract
We consider generalized self-duality equations for U(2r) Yang-Mills theory on R^{4k} with quaternionic structure and self-dual Moyal deformation. We employ the extended ADHM method in 4k dimensions to construct new noncommutative generalizations of the 't Hooft as well as of the BPST instantons. It is shown that in the commutative limit the BPST-type configurations coincide with the standard instantons on HP^n written in local coordinates.
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