Soft factors with AdS radius corrections

Document Type : Regular article


1 Department of Physics, National Taiwan Normal University, Taiwan, R.O.C.

2 Department of Physics, Indian Institute of Science Education and Research Bhopal, Bhopal, India

3 Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea


We review recent developments concerning the soft factorization of scattering amplitudes that arise in the large radius limit of four dimensional Anti-de Sitter (AdS$_4$) spacetimes. This includes the presence of AdS radius dependent corrections of known flat spacetime soft factors and their implication on the relationship between soft theorems and Ward identities of the boundary conformal field theory.


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 [1] A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, [arXiv:1703.05448 [hep-th]]. DOI: 10.48550/arXiv.1703.05448
[2] A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07, 152 (2014). DOI: 10.1007/JHEP07(2014)152
[3] D. Kapec, V. Lysov and A. Strominger, Asymptotic Symmetries of Massless QED in Even Dimensions, Adv. Theor. Math. Phys. 21, 1747-1767 (2017). DOI: 10.4310/ATMP.2017.v21.n7.a6
[4] T. He, P. Mitra, A. P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10, 112 (2014). DOI: 10.1007/JHEP10(2014)112
[5] F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, [arXiv:1404.4091 [hep-th]]. DOI: 10.48550/arXiv.1404.4091
[6] M. Campiglia and A. Laddha, New symmetries for the Gravitational S-matrix, JHEP 04, 076 (2015). DOI: 10.1007/JHEP04(2015)076
[7] T. McLoughlin, A. Puhm and A. M. Raclariu, The SAGEX review on scattering amplitudes chapter 11: soft theorems and celestial amplitudes, J. Phys. A 55 (2022) no.44, 443012. DOI: 10.1088/1751-8121/ac9a40
[8] S. Weinberg, Photons and Gravitons in S-Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass, Phys. Rev. 135, B1049-B1056 (1964). DOI: 10.1103/PhysRev.135.B1049
[9] S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140, B516-B524 (1965). DOI: 10.1103/PhysRev.140.B516
[10] V. Braginsky and K. Thorne, Gravitational-wave bursts with memory and experimental prospects, Nature 327, 123125 (1987). DOI: 10.1038/327123a0
[11] A. Laddha and A. Sen, Logarithmic Terms in the Soft Expansion in Four Dimensions, JHEP 10, 056 (2018). DOI: 10.1007/JHEP10(2018)056
[12] K. Fernandes and A. Mitra, Soft factors from classical scattering on the Reissner-Nordström spacetime, Phys. Rev. D 102, no.10, 105015 (2020). DOI: 10.1103/PhysRevD.102.105015
[13] A. M. Raclariu, Lectures on Celestial Holography, [arXiv:2107.02075 [hep-th]]. DOI: 10.48550/arXiv.2107.02075
[14] S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81 (2021) no.12, 1062. DOI: 10.1140/epjc/s10052-021-09846-7
[15] S. Pasterski, S. H. Shao and A. Strominger, Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere, Phys. Rev. D 96, no.6, 065026 (2017). DOI: 10.1103/PhysRevD.96.065026
[16] S. Pasterski and S. H. Shao, Conformal basis for at space amplitudes, Phys. Rev. D 96, no.6, 065022 (2017). DOI: 10.1103/PhysRevD.96.065022
[17] A. Atanasov, W. Melton, A. M. Raclariu and A. Strominger, Conformal block expansion in celestial CFT, Phys. Rev. D 104, no.12, 126033 (2021). DOI: 10.1103/PhysRevD.104.126033
[18] N. Arkani-Hamed, M. Pate, A. M. Raclariu and A. Strominger, Celestial amplitudes from UV to IR, JHEP 08, 062 (2021). DOI: 10.1007/JHEP08(2021)062
[19] J. M. Maldacena, The Large N limit of superconformal eld theories and supergravity, Adv. Theor. Math. Phys. 2, 231-252 (1998). DOI: 10.4310/ATMP.1998.v2.n2.a1
[20] S. B. Giddings, Flat space scattering and bulk locality in the AdS / CFT correspondence, Phys. Rev. D 61, 106008 (2000). DOI: 10.1103/PhysRevD.61.106008
[21] M. Gary, S. B. Giddings and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80, 085005 (2009). DOI: 10.1103/PhysRevD.80.085005
[22] M. Gary and S. B. Giddings, The Flat space S-matrix from the AdS/CFT correspondence?, Phys. Rev. D 80, 046008 (2009). DOI: 10.1103/PhysRevD.80.046008
[23] J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03, 025 (2011). DOI: 10.1007/JHEP03(2011)025
[24] A. L. Fitzpatrick and J. Kaplan, Scattering States in AdS/CFT, [arXiv:1104.2597 [hep-th]]. DOI: 10.48550/arXiv.1104.2597
[25] A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju and B. C. van Rees, A Natural Language for AdS/CFT Correlators, JHEP 11, 095 (2011). DOI: 10.1007/JHEP11(2011)095
[26] E. Hijano, Flat space physics from AdS/CFT, JHEP 07, 132 (2019). DOI: 10.1007/JHEP07(2019)132
[27] E. Hijano and D. Neuenfeld, Soft photon theorems from CFT Ward identites in the at limit of AdS/CFT, JHEP 11, 009 (2020). DOI: 10.1007/JHEP11(2020)009
[28] N. Banerjee, K. Fernandes and A. Mitra, Soft photon theorem in the small negative cosmological constant limit, JHEP 08, 105 (2021). DOI: 10.1007/JHEP08(2021)105
[29] N. Banerjee, K. Fernandes and A. Mitra, 1/L2 corrected soft photon theorem from a CFT3 Ward identity, JHEP 04 (2023), 055 DOI: 10.1007/JHEP04(2023)055
[30] A. Laddha and A. Sen, Gravity Waves from Soft Theorem in General Dimensions, JHEP 09, 105 (2018). DOI: 10.1007/JHEP09(2018)105
[31] A. Laddha and A. Sen, Observational Signature of the Logarithmic Terms in the Soft Graviton Theorem, Phys. Rev. D 100, no.2, 024009 (2019). DOI: 10.1103/PhysRevD.100.024009
[32] A. Laddha and A. Sen, Classical proof of the classical soft graviton theorem in D > 4, Phys. Rev. D 101, no.8, 084011 (2020). DOI: 10.1103/PhysRevD.101.084011
[33] A. P. Saha, B. Sahoo and A. Sen, Proof of the classical soft graviton theorem in D = 4, JHEP 06, 153 (2020). DOI: 10.1007/JHEP06(2020)153
[34] A. Hamilton, D. N. Kabat, G. Lifschytz and D. A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74, 066009 (2006). DOI: 10.1103/PhysRevD.74.066009
[35] N. Banerjee, A. Bhattacharjee and A. Mitra, Classical Soft Theorem in the AdSSchwarzschild spacetime in small cosmological constant limit, JHEP 01, 038 (2021). DOI: 10.1007/JHEP01(2021)038
[36] B. S. DeWitt and R. W. Brehme, Radiation damping in a gravitational eld, Annals Phys. 9, 220-259 (1960). DOI: 10.1016/0003-4916(60)90030-0
[37] P. C. Peters, Perturbations in the Schwarzschild Metric, Phys. Rev. 146, 938 (1966). DOI: 10.1103/PhysRev.146.938
[38] P. C. Peters, Relativistic gravitational bremsstrahlung, Phys. Rev. D 1, 1559-1571 (1970). DOI: 10.1103/PhysRevD.1.1559
[39] S. J. Kovacs and K. S. Thorne, The Generation of Gravitational Waves. 3. Derivation of Bremsstrahlung Formulas, Astrophys. J. 217, 252-280 (1977). DOI: 10.1086/155576
[40] E. Poisson, A. Pound and I. Vega, The Motion of point particles in curved spacetime, Living Rev. Rel. 14, 7 (2011). DOI: 10.12942/lrr-2011-7
[41] A. Ishibashi and R. M. Wald, Dynamics in nonglobally hyperbolic static space-times. 3. Anti-de Sitter space-time, Class. Quant. Grav. 21, 2981-3014 (2004). DOI: 10.1088/0264-9381/21/12/012
[42] S. Duary, E. Hijano and M. Patra, Towards an IR nite S-matrix in the at limit of AdS/CFT, [arXiv:2211.13711 [hep-th]]. DOI: 10.48550/arXiv.2211.13711
[43] S. Duary, AdS correction to the Faddeev-Kulish state: migrating from the at peninsula, JHEP 05, 079 (2023). DOI: 10.1007/JHEP05(2023)079
[44] Y. Z. Li and J. Mei, Bootstrapping Witten diagrams via dierential representation in Mellin space, JHEP 07, 156 (2023). DOI: 10.1007/JHEP07(2023)156
[45] L. P. de Gioia and A. M. Raclariu, Eikonal approximation in celestial CFT, JHEP 03, 030 (2023). DOI: 10.1007/JHEP03(2023)030
[46] L. P. de Gioia and A. M. Raclariu, Celestial Sector in CFT: Conformally Soft Symmetries, [arXiv:2303.10037 [hep-th]]. DOI: 10.48550/arXiv.2303.10037
[47] A. Lipstein and S. Nagy, Self-Dual Gravity and Color-Kinematics Duality in AdS4, Phys. Rev. Lett. 131, no.8, 081501 (2023). DOI: 10.1103/PhysRevLett.131.081501
[48] S. Atul Bhatkar, Eect of a small cosmological constant on the electromagnetic memory eect, Phys. Rev. D 105 no.12, 124028 (2022). DOI: 10.1103/PhysRevD.105.124028 
Volume 3, Issue 4
November 2023
Pages 5-22
  • Receive Date: 29 September 2023
  • Revise Date: 31 October 2023
  • Accept Date: 31 October 2023