AdS${}_4$ Celestial Symmetries: from Ambitwistor charges to CFT${}_3$ Light-Ray Operators

The $L_{\mathrm{\Lambda }}{w}_{1+\mathrm{\infty }}$ algebra is the cosmological-constant deformation of the celestial $L{w}_{1+\mathrm{\infty }}$ symmetry algebra of gravity, providing an infinite-dimensional extension of the three-dimensional conformal algebra at the AdS${}_4$ boundary. We construct the Hamiltonian charges associated with these symmetries from boundary ambitwistor-space data, using LeBrun’s Heaven on Earth correspondence, and translate them to spacetime via the Penrose transform. We relate the resulting expressions to light-ray operators in the boundary CFT${}_3$, including ANEC operators, their conformal descendants, and their commutators.