Yang-Mills instanton

A Yang-Mills instanton is a finite-action Euclidean gauge field with self-dual or anti-self-dual curvature. On ${\mathbb{R}}^4$, its asymptotic pure gauge defines a map $S_{\infty }^3\to SU(2)$ whose degree is the instanton number.

For an $SU(2)$ connection under a standard trace convention,Its sign depends on orientation and on whether the instanton is self-dual or anti-self-dual.