# Celestial OPE [[0010 Celestial holography|Celestial holography]] relates the [[0078 Collinear limit|collinear]] limit of bulk scattering of massless particles to the [[0030 Operator product expansion|OPE]] of the boundary CFT. This makes **celestial OPE** an essential object in this field. Besides obtaining it from the bulk, it can also be found by [[0036 Conformal bootstrap|bootstrap]] using [[0063 Symmetry of CCFT|symmetries of the celestial CFT]]. This gives a potentially powerful way of understanding bulk scattering itself. ## Refs - [[2019#Fan, Fotopoulos, Taylor]] for YM - [[2019#Pate, Raclariu, Strominger, Yuan]] for EYM - [[2021#Jiang (Aug)]] SUSY EYM and EFT; infinitely many shadow Ward identities - [[2021#Himwich, Pate, Singh]] all spins - [[2021#Jiang (Oct)]]: from WS string theory - [[AdamoMasonSharma2021]]: from [[0330 Twistor theory|twistors]] - [[2023#Krishna, Wang]]: from chiral strings - [[2023#Banerjee, Kulkarni, Paul (Jan)]]: null states and classification for gravity - [[2023#Banerjee, Mandal, Misra, Panda, Paul]]: null states and classification for gauge theory - multi-particle states - [[2024#Guevara, Hu, Pasterski]]: two-particle states found when studying anti-MHV amplitudes - branch-cut - [[2024#Ball]] ## By theory ### Graviton - [[2020#Banerjee, Ghosh, Gonzo]] - [[2020#Banerjee, Ghosh, Paul]] - [[2021#Banerjee, Ghosh, Paul]]: invariance under [[0032 Virasoro algebra|Virasoro]] - [[2023#Ren, Schreiber, Sharma, Wang]]: all order - [[2023#Banerjee, Kulkarni, Paul (Nov)]]: self-dual gravity ### Gluons - [[2020#Ebert, Sharma, Wang]] - [[2020#Banerjee, Ghosh]] - [[2023#Ren, Schreiber, Sharma, Wang]]: all order ## Methods 1. use symmetry [[2019#Pate, Raclariu, Strominger, Yuan]] 2. Mellin transform - bulk scattering amplitude - in the [[0078 Collinear limit|collinear limit]]: Mellin transform the splitting function - see [[2020#Banerjee, Ghosh, Gonzo]] 3. from ambitwister - [[2021#Adamo, Bu, Casali, Sharma]] - SUSY: [[2021#Bu]] ## Between different operators - celestial amplitudes are only a subset - [[0030 Operator product expansion|OPE]] of primary fields in [[2019#Pate, Raclariu, Strominger, Yuan]] - [[2019#Fan, Fotopoulos, Taylor]]: OPE between primary fields and holomorphic currents - OPE of field operators generating all BMS generators (superrotations and supertranslations) in [[2019#Fotopoulos, Stieberger, Taylor, Zhu]] ## Loop level - [[2022#Bhardwaj, Lippstreu, Ren, Spradlin, Srikant, Volovich]]: gluons - [[2023#Krishna]] ## Log CFT - [[2024#Bissi, Donnay, Valsesia]] ## From ambitwistor string theory - e.g. [[2021#Adamo, Bu, Casali, Sharma]] (flat background) and [[2023#Adamo, Bu, Zhu]] (self-dual radiative background) ## Study of infrared divergences - [[2021#Magnea]] - [[2021#Nguyen, Salzer]] - [[NastaseRojasRubio2021]][](https://arxiv.org/pdf/2111.06861.pdf)