IAS Amplitudes Group Meeting

Abstract: Conserved conformal correlation functions play a central role in holography and cosmology, yet their construction becomes increasingly complicated for operators with spin. In this talk, I will show how twistor theory naturally incorporates conformal invariance and conservation through the Penrose transform, providing a systematic framework for constructing spinning correlators in three- and four-dimensional CFTs. The resulting twistor-space expressions are remarkably compact and make double-copy relations between correlators of different spins manifest. These simplifications closely parallel those achieved by the twistor-space formulation of scattering amplitudes. I will show that this analogy extends further: just as scattering amplitudes exhibit remarkable localisation properties in twistor space, so do conformal correlators, as I will illustrate explicitly for three-point functions in four dimensions.