Deriving amplitude relations with differential operators in Anti-de Sitter embedding space

There has been recent interest in extending color-kinematics duality to curved-space. We introduce a representation in which correlators are realized as differential operators - built from AdS symmetry group generators - acting on contact diagrams known as D-functions, which can be used to render the duality manifest. The structure of the flat-space BCJ relations and the commutation properties of Mandelstam invariants suggest that the AdS generalization is obtained by replacing the latter with the multi-particle Casimir invariants of the conformal group.

We will show that this is indeed the case for the AdS extension of the non-linear sigma model (NLSM). The four and six-point correlators are obtained using Feynman rules derived from the embedding space action. We use a combination of D-function identities to demonstrate that the fundamental BCJ relations hold in AdS-NLSM through six points. Using a similar strategy, we show that the BCJ relations hold through four points for AdS-Yang-Mills (YM). We conclude by discussing a possible procedure for realising the double copy in this language.