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

Area of Science:

• Theoretical Physics
• Quantum Gravity
• String Theory

Background:

• Self-dual gravity in flat spacetime is described by the Plebanski action.
• Anti-de Sitter space (AdS) is a key concept in modern theoretical physics, particularly in holography.
• Understanding gravity in AdS backgrounds is crucial for developing quantum gravity theories.

Purpose of the Study:

• To generalize the Plebanski action for self-dual gravity to Euclidean four-dimensional anti-de Sitter space (AdS_{4}).
• To explore the resulting symmetry algebra and its relation to existing structures.
• To establish a double copy construction for Einstein gravity in AdS_{4}.

Main Methods:

• Describing self-dual gravity using a scalar field with cubic interaction and a deformed Poisson bracket.
• Identifying a novel kinematic algebra in AdS_{4}.
• Deriving the three-point interaction vertex from self-dual Yang-Mills via a double copy.

Main Results:

• A simplified generalization of the Plebanski action for self-dual gravity in AdS_{4}.
• Discovery of a novel symmetry algebra, an AdS_{4} version of the kinematic algebra.
• Successful derivation of self-dual gravity in AdS_{4} from self-dual Yang-Mills using a double copy.
• Lifting the kinematic algebra to a deformed w_{1+∞} algebra.

Conclusions:

• Self-dual gravity in AdS_{4} can be elegantly described by a scalar field theory.
• The double copy construction provides a pathway to understand Einstein gravity in AdS_{4}.
• The identified deformed w_{1+∞} algebra connects to celestial holography.