Abstract
We compare and contrast the two approaches of holography in asymptotically flat spacetimes, viz. the co-dimension two Celestial approach based on the Mellin transformation and the co-dimension one Carrollian approach based on the modified Mellin and elucidate how some of the problems of the Celestial approach can be rectified by the Carrollian one. Considering flat holography as a limit from AdS/CFT makes a co-dimension one dual more plausible, and our previous construction of Carrollian correlations from AdS Witten diagrams is testimony to this. In this paper, we show how to generalize our earlier analysis for operators with spin. We work out a large number of explicit non-trivial examples (twelve) and show matching between the limit of AdS4 Witten diagrams and 3d boundary symmetry considerations, thus making the case for the Carrollian dual even stronger.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [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].
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity \( \mathcal{S} \)-matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational Memory, BMS Supertranslations and Soft Theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [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].
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, S.-H. Shao and A. Strominger, Gluon Amplitudes as 2d Conformal Correlators, Phys. Rev. D 96 (2017) 085006 [arXiv:1706.03917] [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].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
A. Bagchi, Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories, Phys. Rev. Lett. 105 (2010) 171601 [arXiv:1006.3354] [INSPIRE].
A. Bagchi and R. Fareghbal, BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries, JHEP 10 (2012) 092 [arXiv:1203.5795] [INSPIRE].
C. Duval, G.W. Gibbons and P.A. Horvathy, Conformal Carroll groups and BMS symmetry, Class. Quant. Grav. 31 (2014) 092001 [arXiv:1402.5894] [INSPIRE].
A. Bagchi, R. Basu, A. Kakkar and A. Mehra, Flat Holography: Aspects of the dual field theory, JHEP 12 (2016) 147 [arXiv:1609.06203] [INSPIRE].
A. Bagchi, S. Detournay and D. Grumiller, Flat-Space Chiral Gravity, Phys. Rev. Lett. 109 (2012) 151301 [arXiv:1208.1658] [INSPIRE].
A. Bagchi, S. Detournay, R. Fareghbal and J. Simón, Holography of 3D Flat Cosmological Horizons, Phys. Rev. Lett. 110 (2013) 141302 [arXiv:1208.4372] [INSPIRE].
H. Afshar et al., Spin-3 Gravity in Three-Dimensional Flat Space, Phys. Rev. Lett. 111 (2013) 121603 [arXiv:1307.4768] [INSPIRE].
H.A. Gonzalez, J. Matulich, M. Pino and R. Troncoso, Asymptotically flat spacetimes in three-dimensional higher spin gravity, JHEP 09 (2013) 016 [arXiv:1307.5651] [INSPIRE].
A. Bagchi, R. Basu, D. Grumiller and M. Riegler, Entanglement entropy in Galilean conformal field theories and flat holography, Phys. Rev. Lett. 114 (2015) 111602 [arXiv:1410.4089] [INSPIRE].
J. Hartong, Holographic Reconstruction of 3D Flat Space-Time, JHEP 10 (2016) 104 [arXiv:1511.01387] [INSPIRE].
A. Bagchi, D. Grumiller and W. Merbis, Stress tensor correlators in three-dimensional gravity, Phys. Rev. D 93 (2016) 061502 [arXiv:1507.05620] [INSPIRE].
H. Jiang, W. Song and Q. Wen, Entanglement Entropy in Flat Holography, JHEP 07 (2017) 142 [arXiv:1706.07552] [INSPIRE].
E. Hijano and C. Rabideau, Holographic entanglement and Poincaré blocks in three-dimensional flat space, JHEP 05 (2018) 068 [arXiv:1712.07131] [INSPIRE].
L. Apolo, H. Jiang, W. Song and Y. Zhong, Swing surfaces and holographic entanglement beyond AdS/CFT, JHEP 12 (2020) 064 [arXiv:2006.10740] [INSPIRE].
S. Banerjee, Null Infinity and Unitary Representation of The Poincaré Group, JHEP 01 (2019) 205 [arXiv:1801.10171] [INSPIRE].
A. Bagchi, S. Banerjee, R. Basu and S. Dutta, Scattering Amplitudes: Celestial and Carrollian, Phys. Rev. Lett. 128 (2022) 241601 [arXiv:2202.08438] [INSPIRE].
A. Bagchi, P. Dhivakar and S. Dutta, AdS Witten diagrams to Carrollian correlators, JHEP 04 (2023) 135 [arXiv:2303.07388] [INSPIRE].
L. Donnay, A. Fiorucci, Y. Herfray and R. Ruzziconi, Carrollian Perspective on Celestial Holography, Phys. Rev. Lett. 129 (2022) 071602 [arXiv:2202.04702] [INSPIRE].
L. Donnay, A. Fiorucci, Y. Herfray and R. Ruzziconi, Bridging Carrollian and celestial holography, Phys. Rev. D 107 (2023) 126027 [arXiv:2212.12553] [INSPIRE].
K. Nguyen and P. West, Carrollian Conformal Fields and Flat Holography, Universe 9 (2023) 385 [arXiv:2305.02884] [INSPIRE].
L.J. Dixon and Y. Shadmi, Testing gluon selfinteractions in three jet events at hadron colliders, Nucl. Phys. B 423 (1994) 3 [hep-ph/9312363] [INSPIRE].
L.J. Dixon, E.W.N. Glover and V.V. Khoze, MHV rules for Higgs plus multi-gluon amplitudes, JHEP 12 (2004) 015 [hep-th/0411092] [INSPIRE].
A. Schreiber, A. Volovich and M. Zlotnikov, Tree-level gluon amplitudes on the celestial sphere, Phys. Lett. B 781 (2018) 349 [arXiv:1711.08435] [INSPIRE].
S. Banerjee, S. Ghosh, P. Pandey and A.P. Saha, Modified celestial amplitude in Einstein gravity, JHEP 03 (2020) 125 [arXiv:1909.03075] [INSPIRE].
A. Bhattacharjee and M. Saha, Entropy of flat space cosmologies from celestial dual, Phys. Rev. D 109 (2024) L041902 [arXiv:2310.02682] [INSPIRE].
J. Salzer, An embedding space approach to Carrollian CFT correlators for flat space holography, JHEP 10 (2023) 084 [arXiv:2304.08292] [INSPIRE].
A. Saha, Carrollian approach to 1 + 3D flat holography, JHEP 06 (2023) 051 [arXiv:2304.02696] [INSPIRE].
A. Saha, w1+∞ and Carrollian holography, JHEP 05 (2024) 145 [arXiv:2308.03673] [INSPIRE].
H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. 7. 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].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-Matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
E. Hijano, Flat space physics from AdS/CFT, JHEP 07 (2019) 132 [arXiv:1905.02729] [INSPIRE].
K. Nguyen, Carrollian conformal correlators and massless scattering amplitudes, JHEP 01 (2024) 076 [arXiv:2311.09869] [INSPIRE].
S. Banerjee, S. Ghosh and R. Gonzo, BMS symmetry of celestial OPE, JHEP 04 (2020) 130 [arXiv:2002.00975] [INSPIRE].
S. Dutta, Stress tensors of 3d Carroll CFTs, Phys. Lett. B 853 (2024) 138672 [arXiv:2212.11002] [INSPIRE].
A. Fiorucci, D. Grumiller and R. Ruzziconi, Logarithmic celestial conformal field theory, Phys. Rev. D 109 (2024) L021902 [arXiv:2305.08913] [INSPIRE].
L. Leblond, Une nouvelle limite non-relativiste du group de Poincaré, Ann. Henri Poincaré 3 (1965) 1.
N.D. Sen Gupta, On an analogue of the Galilei group, Nuovo Cim. A 44 (1966) 512 [INSPIRE].
A. Bagchi, A. Mehra and P. Nandi, Field Theories with Conformal Carrollian Symmetry, JHEP 05 (2019) 108 [arXiv:1901.10147] [INSPIRE].
A. Bagchi, R. Basu, A. Mehra and P. Nandi, Field Theories on Null Manifolds, JHEP 02 (2020) 141 [arXiv:1912.09388] [INSPIRE].
M. Henneaux and P. Salgado-Rebolledo, Carroll contractions of Lorentz-invariant theories, JHEP 11 (2021) 180 [arXiv:2109.06708] [INSPIRE].
J. de Boer et al., Carroll Symmetry, Dark Energy and Inflation, Front. in Phys. 10 (2022) 810405 [arXiv:2110.02319] [INSPIRE].
G. Barnich, K. Nguyen and R. Ruzziconi, Geometric action for extended Bondi-Metzner-Sachs group in four dimensions, JHEP 12 (2022) 154 [arXiv:2211.07592] [INSPIRE].
J. de Boer et al., Carroll stories, JHEP 09 (2023) 148 [arXiv:2307.06827] [INSPIRE].
B. Chen, R. Liu and Y.-F. Zheng, On higher-dimensional Carrollian and Galilean conformal field theories, SciPost Phys. 14 (2023) 088 [arXiv:2112.10514] [INSPIRE].
S. Stieberger and T.R. Taylor, Strings on Celestial Sphere, Nucl. Phys. B 935 (2018) 388 [arXiv:1806.05688] [INSPIRE].
H. Elvang and Y.-T. Huang, Scattering Amplitudes in Gauge Theory and Gravity, Cambridge University Press (2015) [https://doi.org/10.1017/cbo9781107706620].
P.A.M. Dirac, Wave equations in conformal space, Annals Math. 37 (1936) 429 [INSPIRE].
J. Penedones, High Energy Scattering in the AdS/CFT Correspondence, Ph.D. thesis, Faculdade de Ciencias Universidade do Porto (FCUP), Portugal (2007) [arXiv:0712.0802] [INSPIRE].
L.P. de Gioia and A.-M. Raclariu, Eikonal approximation in celestial CFT, JHEP 03 (2023) 030 [arXiv:2206.10547] [INSPIRE].
S.B. Giddings, Flat space scattering and bulk locality in the AdS/CFT correspondence, Phys. Rev. D 61 (2000) 106008 [hep-th/9907129] [INSPIRE].
L.P. de Gioia and A.-M. Raclariu, Celestial Sector in CFT: Conformally Soft Symmetries, arXiv:2303.10037 [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-Matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].
E. Hijano and D. Neuenfeld, Soft photon theorems from CFT Ward identites in the flat limit of AdS/CFT, JHEP 11 (2020) 009 [arXiv:2005.03667] [INSPIRE].
Y.-Z. Li, Notes on flat-space limit of AdS/CFT, JHEP 09 (2021) 027 [arXiv:2106.04606] [INSPIRE].
M.S. Costa, V. Gonçalves and J. Penedones, Spinning AdS Propagators, JHEP 09 (2014) 064 [arXiv:1404.5625] [INSPIRE].
L. Donnay, A. Puhm and A. Strominger, Conformally Soft Photons and Gravitons, JHEP 01 (2019) 184 [arXiv:1810.05219] [INSPIRE].
N. Banerjee, S. Banerjee, S. Atul Bhatkar and S. Jain, Conformal Structure of Massless Scalar Amplitudes Beyond Tree level, JHEP 04 (2018) 039 [arXiv:1711.06690] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
M.D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press (2013) [https://doi.org/10.1017/9781139540940].
D. Nguyen, M. Spradlin, A. Volovich and C. Wen, The Tree Formula for MHV Graviton Amplitudes, JHEP 07 (2010) 045 [arXiv:0907.2276] [INSPIRE].
A. Hodges, New expressions for gravitational scattering amplitudes, JHEP 07 (2013) 075 [arXiv:1108.2227] [INSPIRE].
A. Hodges, A simple formula for gravitational MHV amplitudes, arXiv:1204.1930 [INSPIRE].
S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
A. Puhm, Conformally Soft Theorem in Gravity, JHEP 09 (2020) 130 [arXiv:1905.09799] [INSPIRE].
B.S. DeWitt, Quantum Theory of Gravity. III. Applications of the Covariant Theory, Phys. Rev. 162 (1967) 1239 [INSPIRE].
S. Sannan, Gravity as the Limit of the Type II Superstring Theory, Phys. Rev. D 34 (1986) 1749 [INSPIRE].
A. Brandhuber, J. Plefka and G. Travaglini, The SAGEX Review on Scattering Amplitudes Chapter 1: Modern Fundamentals of Amplitudes, J. Phys. A 55 (2022) 443002 [arXiv:2203.13012] [INSPIRE].
Z. Bern, A. De Freitas and H.L. Wong, On the coupling of gravitons to matter, Phys. Rev. Lett. 84 (2000) 3531 [hep-th/9912033] [INSPIRE].
C.-H. Fu, Y.-J. Du, R. Huang and B. Feng, Expansion of Einstein-Yang-Mills Amplitude, JHEP 09 (2017) 021 [arXiv:1702.08158] [INSPIRE].
J. Plefka and W. Wormsbecher, New relations for graviton-matter amplitudes, Phys. Rev. D 98 (2018) 026011 [arXiv:1804.09651] [INSPIRE].
H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
S. Banerjee, S. Ghosh and P. Paul, MHV graviton scattering amplitudes and current algebra on the celestial sphere, JHEP 02 (2021) 176 [arXiv:2008.04330] [INSPIRE].
Acknowledgments
We would like to thank Daniel Grumiller, Shahin Sheikh-Jabbari, Romain Ruzziconi and especially Shamik Banerjee for helpful discussions.
PD also thanks Tim Adamo, Dionysios Anninos, Alejandra Castro, Chandramouli Chowdhury, Jelle Hartong, Nabil Iqbal, Arthur Lipstein, Prahar Mitra, Silvia Nagy, Gerben Oling, Simon Ross, Joan Simon, Marika Taylor and Mritunjay Verma for comments on the work during and after it was presented in places mentioned below. PD acknowledges the warm hospitality of the University of Cambridge, University of Southampton, Durham University, King’s College London, and the University of Edinburgh during the course of this work.
AB is partially supported by a Swarnajayanti Fellowship from the Science and Engineering Research Board (SERB) under grant SB/SJF/2019-20/08 and SERB grant CRG/2020/002035 and further by a Royal Society of London international exchange grant with the University of Edinburgh. SD thanks partial support from grant SB/SJF/2019-20/08 of AB. PD would like to duly acknowledge the Council of Scientific and Industrial Research (CSIR), New Delhi, for financial assistance through the Senior Research Fellowship (SRF) scheme and the partial support from the Royal Society of London international exchange grant with the University of Edinburgh.
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: 2311.11246
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
Bagchi, A., Dhivakar, P. & Dutta, S. Holography in flat spacetimes: the case for Carroll. J. High Energ. Phys. 2024, 144 (2024). https://doi.org/10.1007/JHEP08(2024)144
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2024)144