Self-Dual Gravity and Color-Kinematics Duality in AdS₄

We show that self-dual gravity in Euclidean four-dimensional anti-de Sitter space (AdS(4)) can be described by a scalar field with a cubic interaction written in terms of a deformed Poisson bracket, providing a remarkably simple generalization of the Plebanski action for self-dual gravity in flat space. This implies a novel symmetry algebra in self-dual gravity, notably an AdS(4) version of the so-called kinematic algebra. We also obtain the three-point interaction vertex of self-dual gravity in AdS(4) from that of self-dual Yang-Mills by replacing the structure constants of the Lie group with the structure constants of the new kinematic algebra, implying that self-dual gravity in AdS(4) can be derived from self-dual Yang-Mills in this background via a double copy. This provides a concrete starting point for defining the double copy for Einstein gravity in AdS(4) by expanding around the self-dual sector. Moreover, we show that the new kinematic Lie algebra can be lifted to a deformed version of the w(1+infinity) algebra, which plays a prominent role in celestial holography.