Analytic Continuation of Complex Gauge Fields[Note 1. This article was presented at the Conference on Nonlinear ...]

The main result of this note treats the problem of unique extension of holomorphic gauge fields across closed subsets of complex Euclidean space, and is based on a corresponding extension theorem for holomorphic vector bundles due to N. P. Buchdahl and the author. Alternatively, let F be a unitary gauge field corresponding to a complex differential form of type (1, 1) (e.g., an anti self‐dual Yang–Mills field on a punctured ball in C 2 ). As a corollary of the main theorem, it is seen that a unique extension of such F , which preserves the curvature type, is obtained if the contraction of F with a holomorphic vector field lies in the image of the ∂¯‐operator of the associated holomorphic vector bundle.