The ADHM construction, which stands for Atiyah-Drinfeld-Hitchin-Manin construction, is a mathematical framework used in theoretical physics and geometry, particularly in the study of instantons in gauge theory. It is a method for constructing solutions to the self-duality equations of gauge fields in four-dimensional Euclidean space, which are fundamental in the study of Yang-Mills theory.
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Take , , , , and , satisfyingRegular data modulo construct framed Anti-self-dual Yang-Mills equations solutions of charge magnitude . The ADHM factorization identity gives an explicit gauge curvature proof. The two complex matrices and the two rectangular maps have real parameters; three real matrix constraints remove , and quotient by removes another , giving dimension at regular points. Degenerate data can describe zero-size singular limits rather than smooth instantons.