On the anti-self dual Yang–Mills side, the solutions, known as instantons, extend to solutions on compactified Euclidean 4-space. On the twistor side, the vector bundles extend from to , and the reality condition on the ASDYM side corresponds to a reality structure on the algebraic bundles on the twistor side. Holomorphic vector bundles over have been extensively studied in the field of algebraic geometry, and all relevant bundles can be generated by the monad construction[3] also known as the ADHM construction, hence giving a classification of instantons.
References
^Dunajski, Maciej (2010). Solitons, instantons, and twistors. Oxford: Oxford University Press. ISBN9780198570622.