On duality of color and kinematics in (A)dS momentum space

TL;DR

The paper investigates whether color-kinematics duality and the double-copy construction extend to AdS momentum-space correlators. It develops two CK formulations—one for integrated correlators and one at the integrand level—and analyzes bi-adjoint scalars and Yang–Mills in various AdS dimensions, using AdS Mandelstam invariants and $p$-integral propagator representations. Key findings show that CK relations for integrated AdS correlators need not yield new BCJ-like constraints, while integrand CK can be arranged via generalized gauge transformations, and AdS KLT/double-copy structures relate YM to bi-adjoint theories with dimension-dependent shifts, though gravity double-copy in AdS is subtler due to Ward identities. The work opens paths to applying AdS CK ideas to cosmological wavefunctions and to exploring loop-level AdS amplitudes, with potential representations in Mellin, celestial, or position space guiding future progress.

Abstract

We explore color-kinematic duality for tree-level AdS/CFT correlators in momentum space. We start by studying the bi-adjoint scalar in AdS at tree-level as an illustrative example. We follow this by investigating two forms of color-kinematic duality in Yang-Mills theory, the first for the integrated correlator in AdS$_4$ and the second for the integrand in general AdS$_{d+1}$. For the integrated correlator, we find color-kinematics does not yield additional relations among $n$-point, color-ordered correlators. To study color-kinematics for the AdS$_{d+1}$ Yang-Mills integrand, we use a spectral representation of the bulk-to-bulk propagator so that AdS diagrams are similar in structure to their flat space counterparts. Finally, we study color KLT relations for the integrated correlator and double-copy relations for the AdS integrand. We find that double-copy in AdS naturally relates the bi-adjoint theory in AdS$_{d+3}$ to Yang-Mills in AdS$_{d+1}$. We also find a double-copy relation at three-points between Yang-Mills in AdS$_{d+1}$ and gravity in AdS$_{d-1}$ and comment on the higher-point generalization. By analytic continuation, these results on AdS/CFT correlators can be translated into statements about the wave function of the universe in de Sitter.

Figures (4)

• Figure 1: AdS Feynman rules for $\phi^3$ theory.
• Figure 2: Four and five point exchange diagram for bi-adjoint scalars.
• Figure 3: Feynman rules for Yang-Mills theory in AdS.
• Figure 4: Four point exchange Witten diagram for Yang-Mills theory.