Double Copy Relation in AdS Space

BCJ amplitude relations for Anti-de Sitter boundary correlators in embedding space

“…In contrast, ref. [94] reports such a squaring relation for the scalar components of the super-gluon and super-graviton multiplet at d = 4. The difference is presumably due to the action of supercharges which introduces a nontrivial dependence on the conformal weight.…”

“…However, imposing color/kinematics duality on integrated, color-ordered momentum space correlators does not seem to yield BCJ relations [92,93]. In contrast to AdS momentum space, scalar Witten diagrams in Mellin space are simple and yield correlation functions that exhibit colourkinematics duality [10,94]. However, with some notable exceptions, see refs.…”

“…[90,95], current state-of-the-art techniques in Mellin space often rely on using supersymmetry to relate scalar correlators to those of spin-1 and spin-2 states [88,[96][97][98][99]. Furthermore, while the Mellin space formalism does lead to a form of color/kinematics duality and double copy [10,94] for (maximally) supersymmetric theories, it does not immediately lead to additional relations between color-ordered correlators. Our results, demonstrating that such relations exist in a position representation of correlation functions, imply that they should also have momentum-and Mellin-space realizations.…”

“…Furthermore, we compare our results with the Mellin space double copy construction of ref. [94], which gives super-graviton AdS boundary correlators on AdS 5 × S 5 in terms of super-gluon AdS boundary correlators on AdS 5 × S 3 . We conclude with a heuristic discussion of double copy procedures for various formulations of AdS boundary correlators in the high energy limit.…”

Bulk locality for scalars and fermions with global symmetry

“…Another interesting direction is to explore the Colour kinematics and Double Copy relations in AdS [55][56][57][58]. In [59] it was pointed out that there is a tension in establishing CK duality in four point amplitudes due to EFT corrections to pure non abelian gauge field.…”