Color/Kinematics Duality in AdS$_4$

TL;DR

This work develops a CK-duality framework for Yang-Mills theory in AdS$_4$ by computing tree-level 4-point amplitudes from Witten diagrams and revealing that, in general, kinematic numerators do not satisfy Jacobi identities away from flat space. A generalized gauge symmetry is shown to exist that yields a unique set of Jacobi-satisfying numerators $ ilde n_s, ilde n_t, ilde n_u$, along with deformed BCJ relations that recover the flat-space results in the appropriate limit. The authors provide compact spinor-helicity expressions for all helicity configurations, including all-plus amplitudes that are nonzero in AdS$_4$, and demonstrate how to reconstruct 3d conformal correlators from the AdS amplitudes via Ward identities. They further discuss the potential gravity double-copy in AdS$_4$ by squaring the Jacobi-satisfying numerators and outline a deformed KLT structure, suggesting a path to AdS$_4$ gravitational amplitudes and boundary stress-tensor correlators. Overall, the paper establishes CK-duality-inspired structure in AdS$_4$, connects bulk amplitudes to boundary correlators, and sets the stage for a gravity double copy in AdS/CFT contexts, with numerous directions for higher-point generalizations and cosmological extensions.

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 AdS$_4$. 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 AdS$_4$ 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 AdS$_4$.

Figures (2)

• Figure 1: The three numerator structures for the color-dressed amplitude. Two of these appear in each color-ordered amplitude.
• Figure 2: Witten diagrams for the color-ordered 4-point AdS amplitude.