On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators

Understand

The AdS boundary correlators and their dual correlation functions of boundary operators have been the main dynamic observables of the holographic duality relating a bulk AdS theory and a boundary conformal field theory.

• We show that tree-level AdS boundary correlators for generic states can be expressed as nonlocal differential operators of a certain structure acting on contact Witten diagrams.
• We further write the boundary correlators in a form that is very similar to flat space amplitudes, with Mandelstam variables replaced by certain combinations of single-state conformal generators, prove that all tree-level AdS boundary correlators have a differential representation, and detail the conversion of such differential expressions to position space.
• We illustrate the construction through the computation of the boundary correlators of scalars coupled to gluons and gravitons; when converted to position space, they reproduce known results.