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 4ball, 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.00765
 arXiv:
 arXiv:1712.00765
 Bibcode:
 2017arXiv171200765L
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Operator Algebras
 EPrint:
 38 pages