Inmathematical physics, the twistor correspondence (also known as Penrose–Ward correspondence) is a bijection between instantonsoncomplexified Minkowski space and holomorphic vector bundlesontwistor space, which as a complex manifoldis, or complex projective 3-space. Twistor space was introduced by Roger Penrose, while Richard Ward formulated the correspondence between instantons and vector bundles on twistor space.
There is a bijection between
where is the complex projective space of dimension .
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.
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