In mathematical physics, the twistor correspondence (also known as Penrose–Ward correspondence) is a bijection between instantons on complexified Minkowski space and holomorphic vector bundles on twistor space, which as a complex manifold is
Twistor space was introduced by Roger Penrose, while Richard Ward formulated the correspondence between instantons and vector bundles on twistor space.
On the twistor side, the vector bundles extend from
, and the reality condition on the ASDYM side corresponds to a reality structure on the algebraic bundles on the twistor side.
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.