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  "body": "\n## Summary\n\nIn 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|1Y4WX4XQWJ]].\nOver 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.\nIn physics they are finite-action solutions of the Euclidean field equations that describe tunnelling between vacua.\nTheir moduli spaces were used by Donaldson to discover new invariants of smooth 4-manifolds.\n\n## Explanations\n\n### L1 human\n\nA connection on a bundle tells how to move internal states, such as the phase of a particle, from point to point, and its curvature measures the twist.\nIn four dimensions the Hodge star sends 2-forms to 2-forms, so a curvature can equal minus its own star.\nInstantons are the connections with this property.\nThey are the most economical way to twist a bundle with a given topology.\nThe basic example is the BPST instanton, a connection for the group $SU(2)$ on $\\R^4$ whose curvature is concentrated near one point.\n",
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