Local Nahm transform and singularity formation of ASD connections

Abstract

This paper develops a local analogue of the ADHM construction, which characterises ASD instantons defined over smooth bounded domains inside Euclidean ${\mathbb{R}}^4$ diffeomorphic to the 4-ball, in terms of infinite dimensional Hilbert spaces and bounded Hermitian linear operators satisfying an analogue of the ADHM equation. Morever, we describe the degeneration of this construction when a family of instantons develops a curvature singularity at the origin.

38 pages

References in corpus (3)

• Gauge Theory in higher dimensions, II
• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
• A survey on Nahm transform