Abstract
In flat space, the color/kinematics duality states that perturbative Yang-Mills amplitudes can be written in such a way that kinematic numerators obey the same Jacobi relations as their color factors. This remarkable duality implies BCJ relations for Yang-Mills amplitudes and underlies the double copy to gravitational amplitudes. In this paper, we find analogous relations for Yang-Mills amplitudes in AdS4. In particular we show that the kinematic numerators of 4-point Yang-Mills amplitudes computed via Witten diagrams in momentum space enjoy a generalised gauge symmetry which can be used to enforce the kinematic Jacobi relation away from the flat space limit, and we derive deformed BCJ relations which reduce to the standard ones in the flat space limit. We illustrate these results using compact new expressions for 4-point Yang-Mills amplitudes in AdS4 and their kinematic numerators in terms of spinors. We also spell out the relation to 3d conformal correlators in momentum space, and speculate on the double copy to graviton amplitudes in AdS4.
Highlights
Scattering amplitudes known as the double copy, which was first seen in the context string amplitudes in the form of the KLT relations [5]
In particular we show that the kinematic numerators of 4-point Yang-Mills amplitudes computed via Witten diagrams in momentum space enjoy a generalised gauge symmetry which can be used to enforce the kinematic Jacobi relation away from the flat space limit, and we derive deformed BCJ relations which reduce to the standard ones in the flat space limit
Using momentum space Witten diagrams, we find that tree-level 4-point amplitudes can be written in terms of kinematic numerators analogous to those of flat space, these numerators are far more complicated for generic polarisations
Summary
Let us begin by reviewing CK duality for tree-level 4-point scattering amplitudes [4, 14]. The conformal correlators can be written in terms of 3-momenta k = k0, k1, k2 , whose sum over all external particles is conserved due to the translational symmetry of the boundary To relate these to Yang-Mills amplitudes in the bulk, it is convenient to lift the 3-momenta to null 4-momenta as follows: kμ = (k0, k1, k2, ik), where k = |k| = −(k0)2 + (k1)2 + (k2)2,. Using this equation, we can eliminate nt in (2.19) to obtain the following relation between the color-ordered AdS amplitudes and kinematic numerators: j1j2j3j4 + Q/t = 1/s + 1/t. The numerators satisfy the kinematic Jacobi relation away from the flat space limit: ns + nt + nu = 0 These numerators can be obtained from (2.23) by setting Q = 0 on the right hand side. We will derive explicit formulas for 4-point AdS amplitudes and their kinematic numerators using Witten diagrams
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