Abstract
We explore a new way of probing scattering of closed strings in AdS5 × S5, which we call ‘the large p limit’. It consists of studying four-point correlators of single-particle operators in \( \mathcal{N} \) = 4 SYM at large N and large ’t Hooft coupling λ, by looking at the regime in which the dual KK modes become short massive strings. In this regime the charge of the single-particle operators is order λ1/4 and the dual KK modes are in between fields and strings. Starting from SUGRA we compute the large p limit of the correlators by introducing an improved AdS5 × S5 Mellin space amplitude, and we show that the correlator is dominated by a saddle point. Our results are consistent with the picture of four geodesics shooting from the boundary of AdS5 × S5 towards a common bulk point, where they scatter as if they were in flat space. The Mandelstam invariants are put in correspondence with the Mellin variables and in turn with certain combinations of cross ratios. At the saddle point the dynamics of the correlator is directly related to the bulk Mellin amplitude, which in the process of taking large p becomes the flat space ten-dimensional S-matrix. We thus learn how to embed the full type IIB S-matrix in the AdS5 × S5 Mellin amplitude, and how to stratify the latter in a large p expansion. We compute the large p limit of all genus zero data currently available, pointing out additional hidden simplicity of known results. We then show that the genus zero resummation at large p naturally leads to the Gross-Mende phase for the minimal area surface around the bulk point. At one-loop, we first uncover a novel and finite Mellin amplitude, and then we show that the large p limit beautifully asymptotes the gravitational S-matrix.
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References
L. Susskind, Holography in the flat space limit, AIP Conf. Proc. 493 (1999) 98 [hep-th/9901079] [INSPIRE].
J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [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].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [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, Scattering States in AdS/CFT, arXiv:1104.2597 [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
V. Gonçalves, Four point function of \( \mathcal{N} \) = 4 stress-tensor multiplet at strong coupling, JHEP 04 (2015) 150 [arXiv:1411.1675] [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].
L. Rastelli and X. Zhou, Mellin amplitudes for AdS5 × S5, Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].
L.F. Alday and A. Bissi, Loop Corrections to Supergravity on AdS5 × S, Phys. Rev. Lett. 119 (2017) 171601 [arXiv:1706.02388] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Quantum Gravity from Conformal Field Theory, JHEP 01 (2018) 035 [arXiv:1706.02822] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Unmixing Supergravity, JHEP 02 (2018) 133 [arXiv:1706.08456] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Loop corrections for Kaluza-Klein AdS amplitudes, JHEP 05 (2018) 056 [arXiv:1711.03903] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Double-trace spectrum of N = 4 supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. D 98 (2018) 126008 [arXiv:1802.06889] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, One-loop amplitudes in AdS5 × S5 supergravity from \( \mathcal{N} \) = 4 SYM at strong coupling, JHEP 03 (2020) 190 [arXiv:1912.01047] [INSPIRE].
F. Aprile et al., Single particle operators and their correlators in free \( \mathcal{N} \) = 4 SYM, JHEP 11 (2020) 072 [arXiv:2007.09395] [INSPIRE].
L. Rastelli and X. Zhou, How to Succeed at Holographic Correlators Without Really Trying, JHEP 04 (2018) 014 [arXiv:1710.05923] [INSPIRE].
L.F. Alday and S. Caron-Huot, Gravitational S-matrix from CFT dispersion relations, JHEP 12 (2018) 017 [arXiv:1711.02031] [INSPIRE].
S. Caron-Huot and A.-K. Trinh, All tree-level correlators in AdS5 × S5 supergravity: hidden ten-dimensional conformal symmetry, JHEP 01 (2019) 196 [arXiv:1809.09173] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal partial wave expansions for N = 4 chiral four point functions, Annals Phys. 321 (2006) 581 [hep-th/0412335] [INSPIRE].
F.A. Dolan, M. Nirschl and H. Osborn, Conjectures for large N superconformal N = 4 chiral primary four point functions, Nucl. Phys. B 749 (2006) 109 [hep-th/0601148] [INSPIRE].
J.A. Minahan, Holographic three-point functions for short operators, JHEP 07 (2012) 187 [arXiv:1206.3129] [INSPIRE].
D.J. Gross and P.F. Mende, The High-Energy Behavior of String Scattering Amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].
B. Basso, F. Coronado, S. Komatsu, H.T. Lam, P. Vieira and D.-l. Zhong, Asymptotic Four Point Functions, JHEP 07 (2019) 082 [arXiv:1701.04462] [INSPIRE].
F. Coronado, Perturbative four-point functions in planar \( \mathcal{N} \) = 4 SYM from hexagonalization, JHEP 01 (2019) 056 [arXiv:1811.00467] [INSPIRE].
F. Coronado, Bootstrapping the Simplest Correlator in Planar \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory to All Loops, Phys. Rev. Lett. 124 (2020) 171601 [arXiv:1811.03282] [INSPIRE].
T. Fleury and S. Komatsu, Hexagonalization of Correlation Functions, JHEP 01 (2017) 130 [arXiv:1611.05577] [INSPIRE].
B. Basso, S. Komatsu and P. Vieira, Structure Constants and Integrable Bootstrap in Planar N = 4 SYM Theory, arXiv:1505.06745 [INSPIRE].
I. Kostov, V.B. Petkova and D. Serban, Determinant Formula for the Octagon Form Factor in N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 122 (2019) 231601 [arXiv:1903.05038] [INSPIRE].
T. Bargheer, F. Coronado and P. Vieira, Octagons I: Combinatorics and Non-Planar Resummations, JHEP 08 (2019) 162 [arXiv:1904.00965] [INSPIRE].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
N. Beisert, R. Hernandez and E. Lopez, A Crossing-symmetric phase for AdS5 × S5 strings, JHEP 11 (2006) 070 [hep-th/0609044] [INSPIRE].
N. Dorey, D.M. Hofman and J.M. Maldacena, On the Singularities of the Magnon S-matrix, Phys. Rev. D 76 (2007) 025011 [hep-th/0703104] [INSPIRE].
T. Bargheer, F. Coronado and P. Vieira, Octagons II: Strong Coupling, arXiv:1909.04077 [INSPIRE].
A.V. Belitsky and G.P. Korchemsky, Exact null octagon, JHEP 05 (2020) 070 [arXiv:1907.13131] [INSPIRE].
A.V. Belitsky and G.P. Korchemsky, Octagon at finite coupling, JHEP 07 (2020) 219 [arXiv:2003.01121] [INSPIRE].
A.V. Belitsky and G.P. Korchemsky, Crossing bridges with strong Szego limit theorem, arXiv:2006.01831 [INSPIRE].
B. Eden, A.C. Petkou, C. Schubert and E. Sokatchev, Partial nonrenormalization of the stress tensor four point function in N = 4 SYM and AdS/CFT, Nucl. Phys. B 607 (2001) 191 [hep-th/0009106] [INSPIRE].
L.F. Alday, A. Bissi and E. Perlmutter, Genus-One String Amplitudes from Conformal Field Theory, JHEP 06 (2019) 010 [arXiv:1809.10670] [INSPIRE].
L.F. Alday, On Genus-one String Amplitudes on AdS5 × S5, arXiv:1812.11783 [INSPIRE].
L.F. Alday and X. Zhou, Simplicity of AdS Supergravity at One Loop, JHEP 09 (2020) 008 [arXiv:1912.02663] [INSPIRE].
A. Bissi, G. Fardelli and A. Georgoudis, Towards All Loop Supergravity Amplitudes on AdS5 × S5, arXiv:2002.04604 [INSPIRE].
D.J. Binder, S.M. Chester, S.S. Pufu and Y. Wang, \( \mathcal{N} \) = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization, JHEP 12 (2019) 119 [arXiv:1902.06263] [INSPIRE].
S.M. Chester, Genus-2 holographic correlator on AdS5 × S5 from localization, JHEP 04 (2020) 193 [arXiv:1908.05247] [INSPIRE].
S.M. Chester, M.B. Green, S.S. Pufu, Y. Wang and C. Wen, Modular invariance in superstring theory from \( \mathcal{N} \) = 4 super-Yang-Mills, JHEP 11 (2020) 016 [arXiv:1912.13365] [INSPIRE].
S.M. Chester and S.S. Pufu, Far Beyond the Planar Limit in Strongly-Coupled \( \mathcal{N} \) = 4 SYM, arXiv:2003.08412 [INSPIRE].
J.M. Drummond, D. Nandan, H. Paul and K.S. Rigatos, String corrections to AdS amplitudes and the double-trace spectrum of \( \mathcal{N} \) = 4 SYM, JHEP 12 (2019) 173 [arXiv:1907.00992] [INSPIRE].
J.M. Drummond, H. Paul and M. Santagata, Bootstrapping string theory on AdS5 × S5, arXiv:2004.07282 [INSPIRE].
J.M. Drummond and H. Paul, One-loop string corrections to AdS amplitudes from CFT, arXiv:1912.07632 [INSPIRE].
N.I. Usyukina and A.I. Davydychev, An Approach to the evaluation of three and four point ladder diagrams, Phys. Lett. B 298 (1993) 363 [INSPIRE].
A.P. Isaev, Multiloop Feynman integrals and conformal quantum mechanics, Nucl. Phys. B 662 (2003) 461 [hep-th/0303056] [INSPIRE].
P. Allendes, B. Kniehl, I. Kondrashuk, E.A.N. Cuello and M.R. Medar, Solution to Bethe-Salpeter equation via Mellin-Barnes transform, Nucl. Phys. B 870 (2013) 243 [arXiv:1205.6257] [INSPIRE].
M.B. Green, J.H. Schwarz and L. Brink, N = 4 Yang-Mills and N = 8 Supergravity as Limits of String Theories, Nucl. Phys. B 198 (1982) 474 [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar, M. Perelstein and J.S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B 530 (1998) 401 [hep-th/9802162] [INSPIRE].
M.B. Green, J.G. Russo and P. Vanhove, Low energy expansion of the four-particle genus-one amplitude in type-II superstring theory, JHEP 02 (2008) 020 [arXiv:0801.0322] [INSPIRE].
J.M. Drummond, Generalised ladders and single-valued polylogarithms, JHEP 02 (2013) 092 [arXiv:1207.3824] [INSPIRE].
L.F. Alday and J. Maldacena, Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space, JHEP 11 (2009) 082 [arXiv:0904.0663] [INSPIRE].
L.F. Alday, D. Gaiotto and J. Maldacena, Thermodynamic Bubble Ansatz, JHEP 09 (2011) 032 [arXiv:0911.4708] [INSPIRE].
L.F. Alday, J. Maldacena, A. Sever and P. Vieira, Y-system for Scattering Amplitudes, J. Phys. A 43 (2010) 485401 [arXiv:1002.2459] [INSPIRE].
R.A. Janik and A. Wereszczynski, Correlation functions of three heavy operators: The AdS contribution, JHEP 12 (2011) 095 [arXiv:1109.6262] [INSPIRE].
Y. Kazama and S. Komatsu, On holographic three point functions for GKP strings from integrability, JHEP 01 (2012) 110 [Erratum JHEP 06 (2012) 150] [arXiv:1110.3949] [INSPIRE].
Y. Kazama and S. Komatsu, Wave functions and correlation functions for GKP strings from integrability, JHEP 09 (2012) 022 [arXiv:1205.6060] [INSPIRE].
Y. Kazama and S. Komatsu, Three-point functions in the SU(2) sector at strong coupling, JHEP 03 (2014) 052 [arXiv:1312.3727] [INSPIRE].
S. Komatsu, Liouville theory, AdS2 string, and three-point functions, J. Phys. A 53 (2020) 283002 [arXiv:1908.03219] [INSPIRE].
J. Caetano and J. Toledo, χ-systems for correlation functions, JHEP 01 (2019) 050 [arXiv:1208.4548] [INSPIRE].
R. Doobary and P. Heslop, Superconformal partial waves in Grassmannian field theories, JHEP 12 (2015) 159 [arXiv:1508.03611] [INSPIRE].
R.B. Paris and D. Kamiski, Asymptotics and Mellin-Barnes Integrals, in Encyclopedia of Mathematics and its Applications 85, Cambridge University Press, Cambridge U.K. (2001) and online at https://www.cambridge.org/9780521790017.
C.R. Mafra and O. Schlotterer, All Order αt Expansion of One-Loop Open-String Integrals, Phys. Rev. Lett. 124 (2020) 101603 [arXiv:1908.09848] [INSPIRE].
J.E. Gerken, A. Kleinschmidt and O. Schlotterer, All-order differential equations for one-loop closed-string integrals and modular graph forms, JHEP 01 (2020) 064 [arXiv:1911.03476] [INSPIRE].
L. Rastelli, K. Roumpedakis and X. Zhou, AdS3 × S3 Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry, JHEP 10 (2019) 140 [arXiv:1905.11983] [INSPIRE].
S. Giusto, R. Russo, A. Tyukov and C. Wen, Holographic correlators in AdS3 without Witten diagrams, JHEP 09 (2019) 030 [arXiv:1905.12314] [INSPIRE].
S. Giusto, R. Russo, A. Tyukov and C. Wen, The CFT6 origin of all tree-level 4-point correlators in AdS3 × S3 , Eur. Phys. J. C 80 (2020) 736 [arXiv:2005.08560] [INSPIRE].
L.F. Alday and X. Zhou, All Tree-Level Correlators for M-theory on AdS7 × S4, Phys. Rev. Lett. 125 (2020) 131604 [arXiv:2006.06653] [INSPIRE].
L.F. Alday and X. Zhou, All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs, arXiv:2006.12505 [INSPIRE].
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Aprile, F., Vieira, P. Large p explorations. From SUGRA to big STRINGS in Mellin space. J. High Energ. Phys. 2020, 206 (2020). https://doi.org/10.1007/JHEP12(2020)206
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DOI: https://doi.org/10.1007/JHEP12(2020)206