Instanton

Summary

In differential geometry, an instanton is a connection on a principal bundle over an oriented Riemannian 4-manifold whose curvature is anti-self-dual for the Hodge star. Over a compact 4-manifold, instantons are absolute minima of the Yang–Mills functional among connections on a given bundle, so they solve the Yang–Mills equations. In physics they are finite-action solutions of the Euclidean field equations that describe tunnelling between vacua. Their moduli spaces were used by Donaldson to discover new invariants of smooth 4-manifolds.