Toupin, Daniel: Twistor Theory and the Resolution of the Googly Problem via Haar Measure Self-Duality on Gr(2,4)

Penrose's twistor programme, initiated in 1967, encodes massless fields through holomorphic structures on projective twistor space PT ≅ CP³. The Penrose–Ward correspondence gives a bijection between anti-self-dual solutions of the vacuum Yang–Mills and Einstein equations and holomorphic vector bundles over PT trivial on every twistor line, but naturally produces only one helicity sector. Completing the construction to include both helicities from a single geometric object is the obstruction Penr