Interpretation of the deformed w_{1+∞}-type algebra in de Sitter gravity

Determine a concrete interpretation, in four-dimensional gravity with positive cosmological constant (de Sitter spacetime, Λ>0), of the deformed w_{1+∞}-type symmetry algebra that acts on gravitational theories with a cosmological constant (the algebra generated by modes w^p_{\bar m,m} obeying the specified deformed commutation relations). Clarify how this algebra is realized in de Sitter gravity and what its physical or holographic meaning is.

Background

The paper establishes that every three-dimensional conformal field theory (CFT3) admits an action of a deformed w_{1+∞}-type algebra generated by the ANEC operator, its conformal descendants, and their commutators, extending tree-level AdS4 results to the quantum regime. This algebra, originally discovered to act on tree-level Einstein gravity with a cosmological constant Λ, deforms the flat-space w_{1+∞} symmetry and is compatible with the AdS4 isometry group SO(3,2).

While the AdS4 (Λ<0) realization is discussed via boundary CFT3 light-ray operators, the case of positive cosmological constant Λ>0 (de Sitter spacetime) is not understood. The authors explicitly note that providing an interpretation of this deformed algebra in the de Sitter gravity context remains unresolved.

References

An interpretation of the \ algebra for gravity in the positive $\Lambda$ de Sitter case remains an open problem.

— EVERY CFT$_3$ HAS AN $ \mathcal{L}_Λw_{1+\infty}$ SYMMETRY  (2603.26459 - Strominger et al., 27 Mar 2026) in Introduction (Section 1)

Therefore, it seems that the same procedure applied in this work to address the unfrozen degrees of freedom can be appropriately used for asymptotically (A)dS spacetimes. We leave this investigation for future work.

— Higher spin dynamics in Weyl reference frame  (2608.16781 - Simone, 17 Aug 2026) in Section 3, subsection “Bracket at linear level”