# Celestial holography Celestial holography is a potential realisation of the holographic principle where 4D scattering amplitudes are believed to be equivalent to a 2D conformal field theory living on the so-called [[0022 Celestial sphere|celestial sphere]]. Similar to [[0001 AdS-CFT|AdS/CFT]], where the isometry group is global AdS is the same as the conformal group of the CFT, here the Lorentz group of four-dimensional Minkowski spacetime is the same as the conformal group of two-dimensional celestial sphere. However, the boundary CFT dual to AdS is Lorentzian, in contrast to the celestial sphere being Euclidean. There are many more things to say about this, but I am using this the rest of the page as a catalogue for this field. A (definitely incomplete) list of relevant topics are given below. Nowadays you can find many good reviews on celestial holography easily. ## General topics - CCFT language - [[0022 Celestial sphere]] - [[0250 Celestial torus]] - [[0148 Conformal basis]] - [[0506 Ambidextrous basis]] - by theory - [[0101 Gluon celestial toolkit]] - [[0262 Celestial amplitude calculations]] - [[2024#Ogawa, Takahashi, Tsuda, Waki]]: WZW model - [[0067 Double copy|double copy]] - [[0198 Celestial double copy]] - properties - [[0063 Symmetry of CCFT]] - [[0215 UV-IR mixing]] - factorisation of singularities - [[CardonaHuang2017]] - unitarity (via optical theorem) - [[2017#Banerjee, Banerjee, Bhatkar, Jain]] - [[LamShao2017]] - locality - [[ChangHuangHuangLi2021]][](https://arxiv.org/pdf/2106.11948.pdf) - [[0038 Celestial conformal blocks]] - [[0312 Grassmannian for CCFT]] - kinematics - [[2022#Mizera, Pasterski]] - [[0366 Classical aspects of CCFT]] - [[0384 4d-2d twistorial correspondence]] - 2d toy models - [[Duary2022]][](https://arxiv.org/abs/2209.02776) - [[KapecTropper2022]][](https://arxiv.org/pdf/2210.16861.pdf) - [[2023#Melton, Narayanan]]: 2D realisation of [[0136 Self-dual Yang-Mills|SDYM]] with a scalar source - higher dimensions - [[CsakiTelemTerning2022]][](https://arxiv.org/pdf/2212.08672.pdf): partially celestial states in $D$ dimensions along $p$-dimensional hyperplane - black holes in CCFT - [[2023#Crawley, Guevara, Himwich, Strominger]] - non-Minkowski spacetimes - [[2023#Adamo, Bu, Zhu]]: self-dual radiative - [[2023#Adamo, Bogna, Mason, Sharma]]: self-dual Taub-NUT - scattering on black hole backgrounds - [[2023#Fernandes, Lin, Mitra]] ## Features and properties - Ward identity of asymptotic symmetries <-> soft theorem - [[0009 Soft theorems]] - e.g. [[0107 Soft gluon symmetry]] - [[0060 Asymptotic symmetry]] <-> [[0063 Symmetry of CCFT]] - e.g. [[0085 Asymptotic symmetry of AdS3]] - [[0106 Ward identity]] - [[0114 Celestial OPE]] <-> [[0078 Collinear limit]] - more generally [[0295 Infrared divergences in scattering amplitude]] - Feynman rules - [[2021#Melton]] ## Extensions/alternatives - [[0289 Celestial superamplitudes]] - [[0516 Celestial correlators]] - connections to AdS/CFT - [[2023#Bu, Seet]] ![[A0008 Stuffed sphere.jpeg]]