2023/04/14 by Arthur Lipstein, Lipstein, Arthur, Silvia Nagy +1 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2304.07141
We show that self-dual gravity in Euclidean four-dimensional Anti-de Sitter space (AdS4) can be described by a minimally coupled scalar field with a cubic interaction written in terms of a deformed Poisson bracket, providing a remarkably simple generalisation of the Plebanski action for self-dual gravity in flat space. This implies a novel symmetry algebra in self-dual gravity, notably an AdS4 version of the so-called kinematic algebra. We also obtain the 3-point interaction vertex of self-dual gravity in AdS4 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 AdS4 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 AdS4 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 w1+∞ algebra, which plays a prominent role in celestial holography.