w1+∞ and Carrollian holography

A bstract In a 1 + 2D Carrollian conformal field theory, the Ward identities of the two local fields S₀^+ S 0 + and S₁^+ S 1 +, entirely built out of the Carrollian conformal stress-tensor, contain respectively up to the leading and the subleading positive helicity soft graviton theorems in the 1 + 3D asymptotically flat space-time. This work investigates how the subsubleading soft graviton theorem can be encoded into the Ward identity of a Carrollian conformal field S₂^+ S 2 +. The operator product expansion (OPE) S₂^+S₂^+ S 2 + S 2 + is constructed using general Carrollian conformal symmetry principles and the OPE commutativity property, under the assumption that any time-independent, non-Identity field that is mutually local with S₀^+ S 0 +, S₁^+ S 1 +, S₂^+ S 2 + has positive Carrollian scaling dimension. It is found that, for this OPE to be consistent, another local field S₃^+ S 3 + must automatically exist in the theory. The presence of an infinite tower of local fields S₊ ₃^+ S k ≥ 3 + is then revealed iteratively as a consistency condition for the S₂^+S₊-₁^+ S 2 + S k − 1 + OPE. The general Sₖ^+Sₗ^+ S k + S l + OPE is similarly obtained and the symmetry algebra manifest in this OPE is found to be the Kac-Moody algebra of the wedge sub-algebra of w 1+ ∞. The Carrollian time-coordinate plays the central role in this purely holographic construction. The 2D Celestial conformally soft graviton primary Hᵏ (z, z) H k z z ¯ is realized to be contained in the Carrollian conformal primary S₁-₊^+ (t, z, z) S 1 − k + t z z ¯. Finally, the existence of the infinite tower of fields Sₖ^+ S k + is shown to be directly related to an infinity of positive helicity soft graviton theorems.