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

TL;DR

This paper investigates the duality between color and kinematics in AdS momentum space, revealing new relations and double-copy structures for correlators and integrands in AdS/CFT, with implications for de Sitter space.

Contribution

It introduces novel duality relations and double-copy structures for AdS correlators and integrands, extending flat space concepts to AdS/CFT context.

Findings

Color-kinematics duality does not produce new relations among integrated correlators in AdS.

Spectral representation enables AdS diagrams to resemble flat space diagrams.

Double-copy relations connect bi-adjoint theory in higher-dimensional AdS to Yang-Mills and gravity in lower dimensions.

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.