From https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011056

The anti–de Sitter/conformal field theory (AdS/CFT) correspondence is a powerful tool that connects theories of quantum gravity with quantum field theories, which describe elementary particles and forces. The conjectured relationship between the two types of theories allows researchers to translate complex problems in one theory into a more tractable problem in the language of the other. However, despite decades of effort, some of the necessary computations are still often hopelessly complicated. Here, we present a new mathematical framework that greatly simplifies these computations.

We can think of AdS space as a box, and the CFT “lives” on its surface. The AdS/CFT duality tells us that we can describe what happens inside the box by looking at the surface and vice versa. In particular, scattering amplitudes inside the box are mapped to certain mathematical objects (correlators) on the surface of the box.

Scattering amplitudes describe the possible outcomes when two particles collide. They are hard to compute, but they are important because they encode the way particles interact in nature, and they also can be directly measured at particle colliders. Here, we elucidate the elegant underlying organizing principles of the correlators and write down all such amplitudes in the class of best-known paradigms of AdS/CFT.

The results provide a wealth of theoretical data that are essential, for example, for analyzing quantum features of gravity in AdS. More importantly, our strategy provides a valuable lesson in further harnessing the computational power of AdS/CFT: Effectively using symmetry principles strips away the intimidating superficial complexities and allows us to focus on the core of the problem, which is often surprisingly simple.

Authors: Luis F. Alday and Xinan Zhou