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A bstract The infrared behavior of gravity in 4D asymptotically flat spacetime exhibits a rich set of symmetries. This has led to a proposed holographic duality between the gravitational $$ \mathcal{S} $$ S -matrix and a dual field theory living on the celestial sphere. Most of our current understanding of the dictionary relies on knowledge of the 4D bulk. As such, identifying intrinsic 2D models that capture the correct symmetries and soft dynamics of 4D gravity is an active area of interest. Here we propose that a 2D generalization of SYK provides an instructive toy model for the soft limit of the gravitational sector in 4D asymptotically flat spacetime. We find that the symmetries and soft dynamics of the 2D SYK model capture the salient features of the celestial theory: exhibiting chaotic dynamics, conformal invariance, and a w 1+ ∞ symmetry. The holographic map from 2D SYK operators to the 4D bulk employs the Penrose twistor transform.
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State-operator correspondence in celestial conformal field theory
A bstract The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere. The states are constructed using the 2D CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross the celestial sphere inside the circle. The BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform. Scattering amplitudes are then given by BPZ inner products between states living on the same circle but with opposite orientations. 2D boundary states are found to encode the same information as their 4D bulk counterparts, but organized in a radically different manner.
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- Award ID(s):
- 1707938
- PAR ID:
- 10302330
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2021
- Issue:
- 9
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP09(2021)132
