Abstract
We study features of celestial CFT correlation functions when the bulk theory is itself a CFT. We show that conformal inversions in the bulk map boost eigenstates to shadow transformed boost eigenstates. This is demonstrated explicitly for the wavefunctions of free massless scalars, and finds interesting applications to building extrapolate dictionaries. Because inversions exchange null infinity and the light cone of the origin, one finds a relation between the massless extrapolate dictionary — involving correlators of operators inserted along null infinity — and the slice-by-slice extrapolate dictionary recently studied by Sleight and Taronna starting from the hyperbolic foliation of de Boer and Solodukhin. Namely, boundary correlators of Sleight and Taronna coincide with celestial amplitudes of shadow transformed boost eigenstates. These considerations are unified by lifting celestial correlators to the Einstein cylinder. This also sheds new light on the extraction of the 𝑆-matrix from the flat limit of AdS/CFT.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. VII. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R.K. Sachs, Gravitational waves in general relativity. VIII. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].
R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [INSPIRE].
E.T. Newman, Heaven and Its Properties, Gen. Rel. Grav. 7 (1976) 107 [INSPIRE].
R. Penrose, The Nonlinear Graviton, Gen. Rel. Grav. 7 (1976) 171 [INSPIRE].
A. Ashtekar, Asymptotic Quantization of the Gravitational Field, Phys. Rev. Lett. 46 (1981) 573 [INSPIRE].
J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
J. de Boer and S.N. Solodukhin, A holographic reduction of Minkowski space-time, Nucl. Phys. B 665 (2003) 545 [hep-th/0303006] [INSPIRE].
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
S. Pasterski, S.-H. Shao and A. Strominger, Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere, Phys. Rev. D 96 (2017) 065026 [arXiv:1701.00049] [INSPIRE].
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].
S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81 (2021) 1062 [arXiv:2108.04801] [INSPIRE].
A.-M. Raclariu, Lectures on Celestial Holography, arXiv:2107.02075 [INSPIRE].
S. Pasterski, M. Pate and A.-M. Raclariu, Celestial Holography, in the proceedings of the Snowmass 2021, Seattle, U.S.A., July 17–26 (2022) [arXiv:2111.11392] [INSPIRE].
C. Cheung, A. de la Fuente and R. Sundrum, 4D scattering amplitudes and asymptotic symmetries from 2D CFT, JHEP 01 (2017) 112 [arXiv:1609.00732] [INSPIRE].
T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05 (2015) 151 [arXiv:1401.7026] [INSPIRE].
T. He and P. Mitra, Covariant Phase Space and Soft Factorization in Non-Abelian Gauge Theories, JHEP 03 (2021) 015 [arXiv:2009.14334] [INSPIRE].
S. Pasterski, A. Puhm and E. Trevisani, Revisiting the conformally soft sector with celestial diamonds, JHEP 11 (2021) 143 [arXiv:2105.09792] [INSPIRE].
A. Ball et al., Uplifting AdS3/CFT2 to flat space holography, JHEP 08 (2019) 168 [arXiv:1905.09809] [INSPIRE].
E. Casali, W. Melton and A. Strominger, Celestial amplitudes as AdS-Witten diagrams, JHEP 11 (2022) 140 [arXiv:2204.10249] [INSPIRE].
L. Iacobacci, C. Sleight and M. Taronna, From celestial correlators to AdS, and back, JHEP 06 (2023) 053 [arXiv:2208.01629] [INSPIRE].
C. Sleight and M. Taronna, Celestial Holography Revisited, arXiv:2301.01810 [INSPIRE].
E. Hijano, Flat space physics from AdS/CFT, JHEP 07 (2019) 132 [arXiv:1905.02729] [INSPIRE].
S. Komatsu, M.F. Paulos, B.C. Van Rees and X. Zhao, Landau diagrams in AdS and S-matrices from conformal correlators, JHEP 11 (2020) 046 [arXiv:2007.13745] [INSPIRE].
R. Penrose, Asymptotic properties of fields and space-times, Phys. Rev. Lett. 10 (1963) 66 [INSPIRE].
A. Guevara, Celestial OPE blocks, arXiv:2108.12706 [INSPIRE].
C. Jorge-Diaz, S. Pasterski and A. Sharma, Celestial amplitudes in an ambidextrous basis, JHEP 02 (2023) 155 [arXiv:2212.00962] [INSPIRE].
A. Atanasov et al., (2, 2) Scattering and the celestial torus, JHEP 07 (2021) 083 [arXiv:2101.09591] [INSPIRE].
E. Crawley, N. Miller, S.A. Narayanan and A. Strominger, State-operator correspondence in celestial conformal field theory, JHEP 09 (2021) 132 [arXiv:2105.00331] [INSPIRE].
J. Cotler, N. Miller and A. Strominger, An integer basis for celestial amplitudes, JHEP 08 (2023) 192 [arXiv:2302.04905] [INSPIRE].
H.S.M. Coxeter, The Representation of Conformal Space on a Quadric, Annals Math. 37 (1936) 416.
R. Penrose and W. Rindler, Spinors and space-time. Volume 2: Spinor and twistor methods in space-time geometry, Cambridge University Press (1988) [https://doi.org/10.1017/CBO9780511524486] [INSPIRE].
R. Penrose, Zero rest mass fields including gravitation: Asymptotic behavior, Proc. Roy. Soc. Lond. A 284 (1965) 159 [INSPIRE].
S. Pasterski, A. Puhm and E. Trevisani, Celestial diamonds: conformal multiplets in celestial CFT, JHEP 11 (2021) 072 [arXiv:2105.03516] [INSPIRE].
H.Z. Chen, R.C. Myers and A.-M. Raclariu, Entanglement, Soft Modes, and Celestial Holography, arXiv:2308.12341 [INSPIRE].
S. Ferrara, A.F. Grillo and G. Parisi, Nonequivalence between conformal covariant wilson expansion in euclidean and minkowski space, Lett. Nuovo Cim. 5S2 (1972) 147 [INSPIRE].
S. Ferrara, A.F. Grillo, G. Parisi and R. Gatto, The shadow operator formalism for conformal algebra. Vacuum expectation values and operator products, Lett. Nuovo Cim. 4S2 (1972) 115 [INSPIRE].
S. Ferrara and G. Parisi, Conformal covariant correlation functions, Nucl. Phys. B 42 (1972) 281 [INSPIRE].
S. Ferrara, A.F. Grillo, G. Parisi and R. Gatto, Covariant expansion of the conformal four-point function, Nucl. Phys. B 49 (1972) 77 [INSPIRE].
D. Simmons-Duffin, Projectors, Shadows, and Conformal Blocks, JHEP 04 (2014) 146 [arXiv:1204.3894] [INSPIRE].
G.R. Brown, J. Gowdy and B. Spence, Celestial twistor amplitudes, Phys. Rev. D 108 (2023) 066009 [arXiv:2212.01327] [INSPIRE].
L. Donnay, A. Puhm and A. Strominger, Conformally Soft Photons and Gravitons, JHEP 01 (2019) 184 [arXiv:1810.05219] [INSPIRE].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
L. Donnay, S. Pasterski and A. Puhm, Goldilocks modes and the three scattering bases, JHEP 06 (2022) 124 [arXiv:2202.11127] [INSPIRE].
L. Donnay, S. Pasterski and A. Puhm, Asymptotic Symmetries and Celestial CFT, JHEP 09 (2020) 176 [arXiv:2005.08990] [INSPIRE].
A. Puhm, Conformally Soft Theorem in Gravity, JHEP 09 (2020) 130 [arXiv:1905.09799] [INSPIRE].
N. Ogawa, T. Takayanagi, T. Tsuda and T. Waki, Wedge holography in flat space and celestial holography, Phys. Rev. D 107 (2023) 026001 [arXiv:2207.06735] [INSPIRE].
M. Fukada and A. Miyata, Mixed boundary conditions and Double-trace like deformations in Celestial holography and Wedge-like holography, arXiv:2305.10779 [INSPIRE].
S. Pasterski and A. Puhm, Shifting spin on the celestial sphere, Phys. Rev. D 104 (2021) 086020 [arXiv:2012.15694] [INSPIRE].
M. Luscher and G. Mack, Global Conformal Invariance in Quantum Field Theory, Commun. Math. Phys. 41 (1975) 203 [INSPIRE].
S. Rychkov, EPFL Lectures on Conformal Field Theory in 𝐷 ≥ 3 Dimensions, arXiv:1601.05000 [https://doi.org/10.1007/978-3-319-43626-5] [INSPIRE].
S. Caron-Huot et al., Detectors in weakly-coupled field theories, JHEP 04 (2023) 014 [arXiv:2209.00008] [INSPIRE].
C.-M. Chang et al., Shadow celestial amplitudes, JHEP 02 (2023) 017 [arXiv:2210.04725] [INSPIRE].
S. Caron-Huot, Holographic cameras: an eye for the bulk, JHEP 03 (2023) 047 [arXiv:2211.11791] [INSPIRE].
K. Costello, N.M. Paquette and A. Sharma, Top-Down Holography in an Asymptotically Flat Spacetime, Phys. Rev. Lett. 130 (2023) 061602 [arXiv:2208.14233] [INSPIRE].
K. Costello, N.M. Paquette and A. Sharma, Burns space and holography, JHEP 10 (2023) 174 [arXiv:2306.00940] [INSPIRE].
S.W. Hawking, D.N. Page and C.N. Pope, Quantum Gravitational Bubbles, Nucl. Phys. B 170 (1980) 283 [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: Energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
C. Córdova and S.-H. Shao, Light-ray Operators and the BMS Algebra, Phys. Rev. D 98 (2018) 125015 [arXiv:1810.05706] [INSPIRE].
Y. Hu and S. Pasterski, Celestial conformal colliders, JHEP 02 (2023) 243 [arXiv:2211.14287] [INSPIRE].
Y. Hu and S. Pasterski, Detector operators for celestial symmetries, JHEP 12 (2023) 035 [arXiv:2307.16801] [INSPIRE].
I.Y. Arefeva, L.D. Faddeev and A.A. Slavnov, Generating Functional for the s Matrix in Gauge Theories, Teor. Mat. Fiz. 21 (1974) 311 [INSPIRE].
S. Kim, P. Kraus, R. Monten and R.M. Myers, S-matrix path integral approach to symmetries and soft theorems, JHEP 10 (2023) 036 [arXiv:2307.12368] [INSPIRE].
S. Caron-Huot, M. Giroux, H.S. Hannesdottir and S. Mizera, What can be measured asymptotically?, JHEP 01 (2024) 139 [arXiv:2308.02125] [INSPIRE].
L.P. de Gioia and A.-M. Raclariu, Celestial Sector in CFT: Conformally Soft Symmetries, arXiv:2303.10037 [INSPIRE].
J. Kulp and S. Pasterski, Multiparticle States for the Flat Hologram, to appear.
L. Ciambelli, S. Pasterski and E. Tabor, Radiation in Holography, to appear.
M. Gary, S.B. Giddings and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80 (2009) 085005 [arXiv:0903.4437] [INSPIRE].
A.L. Fitzpatrick, E. Katz, D. Poland and D. Simmons-Duffin, Effective Conformal Theory and the Flat-Space Limit of AdS, JHEP 07 (2011) 023 [arXiv:1007.2412] [INSPIRE].
K. Costello and N.M. Paquette, Celestial holography meets twisted holography: 4d amplitudes from chiral correlators, JHEP 10 (2022) 193 [arXiv:2201.02595] [INSPIRE].
K. Costello and N.M. Paquette, Associativity of One-Loop Corrections to the Celestial Operator Product Expansion, Phys. Rev. Lett. 129 (2022) 231604 [arXiv:2204.05301] [INSPIRE].
W. Bu and E. Casali, The 4d/2d correspondence in twistor space and holomorphic Wilson lines, JHEP 11 (2022) 076 [arXiv:2208.06334] [INSPIRE].
K. Costello, T. Dimofte and D. Gaiotto, Boundary Chiral Algebras and Holomorphic Twists, Commun. Math. Phys. 399 (2023) 1203 [arXiv:2005.00083] [INSPIRE].
K.J. Costello, Quantizing local holomorphic field theories on twistor space, arXiv:2111.08879 [INSPIRE].
N.M. Paquette and B.R. Williams, Koszul duality in quantum field theory, arXiv:2110.10257 [INSPIRE].
K. Costello and N.M. Paquette, Twisted Supergravity and Koszul Duality: A case study in AdS3, Commun. Math. Phys. 384 (2021) 279 [arXiv:2001.02177] [INSPIRE].
S. Pasterski, Implications of Superrotations, Phys. Rept. 829 (2019) 1 [arXiv:1905.10052] [INSPIRE].
Acknowledgments
We are grateful to Simon Caron-Huot, Jordan Cotler, Yangrui Hu, Justin Kulp, Prahar Mitra, and Rob Myers for useful discussions. The research of SP is supported by the Celestial Holography Initiative at the Perimeter Institute for Theoretical Physics and by the Simons Collaboration on Celestial Holography. AS is supported by a Black Hole Initiative fellowship, funded by the Gordon and Betty Moore Foundation and the John Templeton Foundation. SP and EJ’s research at the Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Industry Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2310.02186
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Jørstad, E., Pasterski, S. & Sharma, A. Equating extrapolate dictionaries for massless scattering. J. High Energ. Phys. 2024, 228 (2024). https://doi.org/10.1007/JHEP02(2024)228
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2024)228