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

TL;DR

This work computes real-time boundary Wightman functions in AdS$_4$/CFT$_3$ for scalars, photons/gluons, and gravitons via bulk EOM methods, analytic continuation, and eventually a twistor-space reformulation. A central result is that four-point exchange with spacelike middle momenta factorizes into a product of three-point functions, matching Wightman conformal partial waves and enabling Euclidean reconstruction without nested bulk integrals. In twistor space, the authors obtain compact expressions for two-, three-, and four-point functions, establish clear double copy relations between YM and GR correlators, and illustrate how gravity correlators arise as squares of gauge-theory results in Schwinger parameter space. The paper lays groundwork for a twistor-based conformal bootstrap for AdS/CFT and opens avenues toward higher-point functions, general dimensions, and loop corrections. Overall, the approach provides a streamlined, algebraic route to real-time holographic correlators with elegant twistor-space structure and a transparent gauge/gravity correspondence.

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.

Figures (1)

• Figure 1: Recovering the full correlator from just the special kinematics Wightman function. Note that there is not a single nested bulk integral in sight in this procedure! Once we have the EAdS$_4$ correlator, one can in principle obtain any Lorentzian correlator in any desired kinematics.