0063 Symmetry of CCFT - otherworldlines

# Symmetry of CCFT The symmetry group of a [[0010 Celestial holography|celestial CFT]] is much larger than that of an ordinary CFT because of the [[0060 Asymptotic symmetry|asymptotic symmetries]] and [[0009 Soft theorems|soft theorems]]. Recently, people have discovered the so-called celestial chiral algebra, which is [[0328 w(1+infinity)|w(1+infinity)]] algebra for gravity and S-algebra for gauge theory. ## Symmetry ###### Einstein gravity - Full group: **Extended [[0064 BMS group|BMS group]]** - = Virasoro + Supertranslations - Global part: - Double cover of the 4d Lorentz group is identified with the $SL(2,C)$ global conformal group of the CS. - $SL(2, C)$ is the *global* conformal group in 2d CFT - The larger group containing it is Virasoro times Virasoro (or local conformal group) - $SL(2, C)$ is also the Lorentz group - Note that $sl(2,C)$ is three dimensional when viewed as a complex Lie algebra, but six dimensional when viewed as a real Lie algebra. - It is conjectured that coupling to gravity makes scattering amplitudes invariant under the larger group: Virasoro - in (2,2) signature, the Lorentz group is $S L(2, \mathbb{R})_z \times S L(2, \mathbb{R})_{\bar{z}}$ ###### Yang-Mills - see [[0101 Gluon celestial toolkit]] - current is the conformal soft limit of conformal operators ## 2d diffeomorphism - see [[Schwarz2022]][](https://arxiv.org/abs/2208.13304) and refs therein ## History - [[0064 BMS group]]: [[1962#Bondi, van der Burg, Metzner]] and [[1962#Sachs]] - [[2003#de Boer, Solodukhin]] early proposal of flat holography - Extended BMS: [[BarnichTroessaert2009]] - [[2013#Strominger (Dec)]] shows that extended BMS is also a symmetry of the S matrix for elementary particles and gravitons