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$w_{1+\infty}$ and Carrollian Holography
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abstract
In a $1+2$D Carrollian conformal field theory, the Ward identities of the two local fields $S^+_0$ and $S^+_1$, 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 $1+3$D 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 $S^+_2$. The operator product expansion (OPE) $S^+_2S^+_2$ 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 $S^+_0,S^+_1,S^+_2$ has positive Carrollian scaling dimension. It is found that, for this OPE to be consistent, another local field $S^+_3$ must automatically exist in the theory. The presence of an infinite tower of local fields $S^+_{k\geq3}$ is then revealed iteratively as a consistency condition for the $S^+_2S^+_{k-1}$ OPE. The general $S^+_kS^+_l$ 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 $w_{1+\infty}$. The Carrollian time-coordinate plays the central role in this purely holographic construction. The 2D Celestial conformally soft graviton primary $H^k(z,\bar{z})$ is realized to be contained in the Carrollian conformal primary $S_{1-k}^+(t,z,\bar{z})$. Finally, the existence of the infinite tower of fields $S^+_{k}$ is shown to be directly related to an infinity of positive helicity soft graviton theorems.
Forward citations
Cited by 6 Pith papers
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Light and Shadow OPEs: A Carroll Symmetric Approach to Flat Holography
Translation symmetry alone fixes the scaling dimension and leading OPE coefficient for light-transformed Carrollian primaries, matching known graviton, gluon, and Einstein-Yang-Mills results.
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Non-Lorentzian Supergravity and Kinematical Superalgebras
Supersymmetric extensions of extended kinematical algebras are classified via semigroup expansion, and non-degenerate Chern-Simons supergravity actions are constructed in three dimensions.
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Infinite towers of 2d symmetry algebras from Carrollian limit of 3d CFT
The Carrollian limit of CFT3 operator products yields towers of sl(2,C) blocks that reproduce conformally soft photon and graviton theorems and the S and w1+∞ celestial symmetry algebras.
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Modular matrices of 2d Carrollian and warped CFTs
Explicit modular S and T matrices are derived for Carrollian (bms3) and warped CFT characters, with checks of S squared and unitarity.
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Quantization of Carrollian fermions
A first interacting 4D Carrollian Yukawa theory is constructed, showing ultralocal fermion-scalar interactions and one-loop beta functions with mostly Gaussian fixed points.
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Lectures on Carrollian Holography
Massless scattering amplitudes, including gravitons, can be recast as correlators of a carrollian conformal field theory on null infinity, but the non-perturbative bootstrap program remains incomplete.
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