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 AdS4 and the second for the integrand in general AdSd+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 AdSd+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 AdSd+3 to Yang-Mills in AdSd+1. We also find a double-copy relation at three-points between Yang-Mills in AdSd+1 and gravity in AdSd−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.
Highlights
One motivation to study holographic correlators in momentum space comes from their close connection to the wave function of the universe [37,38,39], which can be used to compute late-time cosmological correlators
To study color-kinematics for the AdSd+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
In this work we explored the viability of color-kinematics and double-copy in AdS momentum space
Summary
Let us recall that the bi-adjoint scalar theory consists of scalars φaA which are charged under two different SU(N ) global symmetries (see [51,52,53] and references therein). We will use lowercase and capital Latin letters to distinguish the two groups. The action for this theory is simple and takes the following form: Sbi-adjoint = −. We have added the Ricci scalar with an arbitrary ξ to be general and will later fix it so the scalar is conformally coupled. The scalar φaA is dual to a boundary operator OaA with conformal dimension ∆ = d/2 + ν where. We need the bulk-to-bulk propagator for scalars in AdS: Gsνc(k, z1, z2). √ where J is the modified Bessel function of the first kind and k ≡ |k| = k2 is the norm of the boundary momenta k.
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