w1+∞ and Carrollian holography

Abstract

Abstract In a 1 + 2D Carrollian conformal field theory, the Ward identities of the two local fields $$ {S}_0^{+} $$ S 0 + and $$ {S}_1^{+} $$ 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 $$ {S}_2^{+} $$ S 2 + . The operator product expansion (OPE) $$ {S}_2^{+}{S}_2^{+} $$ 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 $$ {S}_0^{+} $$ S 0 + , $$ {S}_1^{+} $$ S 1 + , $$ {S}_2^{+} $$ S 2 + has positive Carrollian scaling dimension. It is found that, for this OPE to be consistent, another local field $$ {S}_3^{+} $$ S 3 + must automatically exist in the theory. The presence of an infinite tower of local fields $$ {S}_{k\ge 3}^{+} $$ S k ≥ 3 + is then revealed iteratively as a consistency condition for the $$ {S}_2^{+}{S}_{k-1}^{+} $$ S 2 + S k − 1 + OPE. The general $$ {S}_k^{+}{S}_l^{+} $$ 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 w1+∞. The Carrollian time-coordinate plays the central role in this purely holographic construction. The 2D Celestial conformally soft graviton primary $$ {H}^k\left(z,\overline{z}\right) $$ H k z z ¯ is realized to be contained in the Carrollian conformal primary $$ {S}_{1-k}^{+}\left(t,z,\overline{z}\right) $$ S 1 − k + t z z ¯ . Finally, the existence of the infinite tower of fields $$ {S}_k^{+} $$ S k + is shown to be directly related to an infinity of positive helicity soft graviton theorems.