AdS$_4$ Boundary Wightman functions in Twistor Space: Factorization, Conformal blocks and a Double Copy

Abstract

We study real-time holographic four point Wightman functions involving scalars, photons, gluons and gravitons in the Poincare patch of AdS$_4$. We show that when the momenta of the middle two operators are spacelike, four-point exchange Wightman functions factorize into a product of three-point functions. This expression coincides with a Wightman conformal partial wave corresponding to the operator dual to the exchanged particle in the bulk. Further, we discuss and explicitly show how these results can be analytically continued to obtain Euclidean AdS correlators up to contact diagrams and avoid the need to perform any nested bulk point integrals in contrast to the traditional Witten diagram approach. We then translate our results to twistor space taking first steps towards a twistor space reformulation of four point Wightman functions. For conformally coupled scalars interacting with a cubic potential, we obtain a beautiful form for four and five point functions. For the interesting case of Yang-Mills theory and Einstein gravity, we derive a simple double copy relation. This is easiest to see when correlators are expressed in twistor space using Schwinger parameterization where the graviton correlator is simply the square of its gluon counterpart.