Self-Dual Gravity and Color-Kinematics Duality in AdS_{4}.

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+∞} algebra, which plays a prominent role in celestial holography.

The Super-Stückelberg procedure and dS in pure supergravity.

Understanding de Sitter space in supergravity-and string theory-has led to an intense amount of work for more than two decades, largely motivated by the discovery of the accelerated expansion of the Universe in 1998. In this paper, we consider a non-trivial generalization of unimodular gravity to minimal N = 1 supergravity, which allows for de Sitter solutions without the need of introducing any matter. We formulate a superspace version of the Stückelberg procedure, which restores diffeomorphism and local supersymmetry invariance. This introduces the goldstino associated with spontaneous breaking of supersymmetry in a natural way. The cosmological constant and gravitino mass are related to the vacuum expectation value of the components of a Lagrange multiplier imposing a super-unimodularity condition.