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 Sk≥ 3⁺ S k ≥ 3 + is then revealed iteratively as a consistency condition for the S₂⁺Sₖ₋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,z̄) H k z z ¯ is realized to be contained in the Carrollian conformal primary S₁₋ₖ⁺(t,z,z̄) 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.