Color/Kinematics Duality in AdS$_4$

TL;DR

This paper extends the color/kinematics duality from flat space to AdS$_4$, revealing new relations for Yang-Mills amplitudes in curved spacetime and exploring their implications for gravity via the double copy.

Contribution

It demonstrates the existence of generalized gauge symmetries and deformed BCJ relations for Yang-Mills amplitudes in AdS$_4$, providing explicit formulas and connections to conformal correlators.

Findings

Kinematic numerators in AdS$_4$ obey generalized gauge symmetries.

Deformed BCJ relations reduce to flat space in the appropriate limit.

Explicit 4-point amplitude expressions in AdS$_4$ using spinors.

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$_4$.