Abstract
We propose a formula relating scattering S-matrix amplitudes to correlators of a conformal field theory. The proposal implements a flat limit of the field theory, providing an indirect microscopic description of gravitational theories with asymptotically flat boundary conditions. The formula is valid for both massive and massless external particles, and reduces to existing expressions in the literature when all particles are either simultaneously massless or massive. We test the result in various (2 + 1)-dimensional examples such as simple BMS3 invariant correlators and blocks. We also study two-point correlators in conformal field theory deficit states to obtain known expressions for nontrivial scattering in asymptotically flat conical geometries.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. ’t Hooft, The holographic principle: opening lecture, Subnucl. Ser.37 (2001) 72 [hep-th/0003004] [INSPIRE].
L. Susskind, The world as a hologram, J. Math. Phys.36 (1995) 6377 [hep-th/9409089] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [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].
M. Gary and S.B. Giddings, The flat space S-matrix from the AdS/CFT correspondence?, Phys. Rev.D 80 (2009) 046008 [arXiv:0904.3544] [INSPIRE].
S.B. Giddings, The boundary S matrix and the AdS to CFT dictionary, Phys. Rev. Lett.83 (1999) 2707 [hep-th/9903048] [INSPIRE].
V. Balasubramanian, S.B. Giddings and A.E. Lawrence, What do CFTs tell us about Anti-de Sitter space-times?, JHEP03 (1999) 001 [hep-th/9902052] [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Scattering states in AdS/CFT, arXiv:1104.2597 [INSPIRE].
J.M. Maldacena and G.L. Pimentel, On graviton non-Gaussianities during inflation, JHEP09 (2011) 045 [arXiv:1104.2846] [INSPIRE].
S. Raju, New recursion relations and a flat space limit for AdS/CFT correlators, Phys. Rev.D 85 (2012) 126009 [arXiv:1201.6449] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-matrix, JHEP10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Unitarity and the holographic S-matrix, JHEP10 (2012) 032 [arXiv:1112.4845] [INSPIRE].
M.F. Paulos et al., The S-matrix bootstrap. Part I: QFT in AdS, JHEP11 (2017) 133 [arXiv:1607.06109] [INSPIRE].
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. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev.D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].
S. Deser and R. Jackiw, Classical and quantum scattering on a cone, Commun. Math. Phys.118 (1988) 495 [INSPIRE].
G. ’t Hooft, Nonperturbative two particle scattering amplitudes in (2 + 1)-dimensional quantum gravity, Commun. Math. Phys.117 (1988) 685 [INSPIRE].
J. Spinally, E.R. Bezerra de Mello and V.B. Bezerra, Relativistic quantum scattering on a cone, Class. Quant. Grav.18 (2001) 1555 [gr-qc/0012103] [INSPIRE].
R.K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond.A 270 (1962) 103.
A. Campoleoni, H.A. Gonzalez, B. Oblak and M. Riegler, BMS modules in three dimensions, Int. J. Mod. Phys.A 31 (2016) 1650068 [arXiv:1603.03812] [INSPIRE].
E. Hijano and C. Rabideau, Holographic entanglement and Poincaré blocks in three-dimensional flat space, JHEP05 (2018) 068 [arXiv:1712.07131] [INSPIRE].
E. Hijano, Semi-classical BMS 3blocks and flat holography, JHEP10 (2018) 044 [arXiv:1805.00949] [INSPIRE].
A. Bagchi, A. Saha and Zodinmawia, BMS characters and modular invariance, arXiv:1902.07066 [INSPIRE].
T. Araujo, Remarks on BMS 3invariant field theories: correlation functions and nonunitary CFTs, Phys. Rev.D 98 (2018) 026014 [arXiv:1802.06559] [INSPIRE].
E. Witten, Three-Dimensional Gravity Revisited, arXiv:0706.3359 [INSPIRE].
A. Castro et al., The gravity dual of the Ising model, Phys. Rev.D 85 (2012) 024032 [arXiv:1111.1987] [INSPIRE].
G. Barnich, A. Gomberoff and H.A. González, Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory, Phys. Rev.D 87 (2013) 124032 [arXiv:1210.0731] [INSPIRE].
G. Barnich and H.A. Gonzalez, Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity, JHEP05 (2013) 016 [arXiv:1303.1075] [INSPIRE].
D. Kabat, G. Lifschytz and D.A. Lowe, Constructing local bulk observables in interacting AdS/CFT, Phys. Rev.D 83 (2011) 106009 [arXiv:1102.2910] [INSPIRE].
D. Kabat and G. Lifschytz, Locality, bulk equations of motion and the conformal bootstrap, JHEP10 (2016) 091 [arXiv:1603.06800] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev.140 (1965) B516 [INSPIRE].
D. Carney, L. Chaurette, D. Neuenfeld and G. Semenoff, On the need for soft dressing, JHEP09 (2018) 121 [arXiv:1803.02370] [INSPIRE].
D. Carney, L. Chaurette, D. Neuenfeld and G.W. Semenoff, Dressed infrared quantum information, Phys. Rev.D 97 (2018) 025007 [arXiv:1710.02531] [INSPIRE].
A. Lewkowycz, G.J. Turiaci and H. Verlinde, A CFT perspective on gravitational dressing and bulk locality, JHEP01 (2017) 004 [arXiv:1608.08977] [INSPIRE].
N. Anand et al., An exact operator that knows its location, JHEP02 (2018) 012 [arXiv:1708.04246] [INSPIRE].
H. Chen, J. Kaplan and U. Sharma, AdS 3reconstruction with general gravitational dressings, arXiv:1905.00015 [INSPIRE].
J. Cotler et al., Entanglement wedge reconstruction via universal recovery channels, arXiv:1704.05839 [INSPIRE].
C.-F. Chen, G. Penington and G. Salton, Entanglement wedge reconstruction using the Petz map, arXiv:1902.02844 [INSPIRE].
A. Higuchi, Symmetric tensor spherical harmonics on the N sphere and their application to the de Sitter group SO(N, 1), J. Math. Phys. 28 (1987) 1553 [Erratum ibid.43 (2002) 6385] [INSPIRE].
G. Mack, D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary dual resonance models. Scalar amplitudes, arXiv:0907.2407 [INSPIRE].
G. Mack, D-dimensional Conformal Field Theories with anomalous dimensions as dual resonance models, Bulg. J. Phys.36 (2009) 214 [arXiv:0909.1024] [INSPIRE].
G. Barnich and B. Oblak, Notes on the BMS group in three dimensions: I. Induced representations, JHEP06 (2014) 129 [arXiv:1403.5803] [INSPIRE].
D. Harlow and D. Stanford, Operator dictionaries and wave functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
A. Bagchi, M. Gary and Zodinmawia, The nuts and bolts of the BMS bootstrap, Class. Quant. Grav.34 (2017) 174002 [arXiv:1705.05890] [INSPIRE].
E.S. Moreira, Jr., Massive quantum fields in a conical background, Nucl. Phys.B 451 (1995) 365 [hep-th/9502016] [INSPIRE].
I.Ya. Aref’eva and M.A. Khramtsov, AdS/CFT prescription for angle-deficit space and winding geodesics, JHEP04 (2016) 121 [arXiv:1601.02008] [INSPIRE].
S. Hollands and R.M. Wald, Quantum fields in curved spacetime, Phys. Rept.574 (2015) 1 [arXiv:1401.2026] [INSPIRE].
A. Vilenkin, Cosmic strings and domain walls, Phys. Rept.121 (1985) 263 [INSPIRE].
J.R. Gott, III, Gravitational lensing effects of vacuum strings: Exact solutions, Astrophys. J.288 (1985) 422 [INSPIRE].
E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Semiclassical Virasoro blocks from AdS 3gravity, JHEP12 (2015) 077 [arXiv:1508.04987] [INSPIRE].
A. Maloney, H. Maxfield and G.S. Ng, A conformal block Farey tail, JHEP06 (2017) 117 [arXiv:1609.02165] [INSPIRE].
E. Hijano and C. Rabideau, to appear.
T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP05 (2015) 151 [arXiv:1401.7026] [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
J. Maldacena, D. Simmons-Duffin and A. Zhiboedov, Looking for a bulk point, JHEP01 (2017) 013 [arXiv:1509.03612] [INSPIRE].
S. Gradshteyn, and M. Ryzhiz, Table of integrals, series, and products, Academic Press, U.S.A. (2015).
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1905.02729
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Hijano, E. Flat space physics from AdS/CFT. J. High Energ. Phys. 2019, 132 (2019). https://doi.org/10.1007/JHEP07(2019)132
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2019)132