Abstract
We report a result for the third-order correction in 1/N expansion to the four-point correlator of the stress tensor multiplet in \( \mathcal{N} \) = 4 super Yang-Mills theory at large ’t Hooft coupling, which corresponds to the two-loop scattering of four gravitons in the dual AdS5 × S5 supergravity. This is obtained by bootstrapping an educated ansatz based on intuitions from the hidden 10-dimensional conformal symmetry.
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References
P. Heslop, The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators, J. Phys. A 55 (2022) 443009 [arXiv:2203.13019] [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].
G. Arutyunov, F.A. Dolan, H. Osborn and E. Sokatchev, Correlation functions and massive Kaluza-Klein modes in the AdS / CFT correspondence, Nucl. Phys. B 665 (2003) 273 [hep-th/0212116] [INSPIRE].
G. Arutyunov, S. Frolov, R. Klabbers and S. Savin, Towards 4-point correlation functions of any \( \frac{1}{2} \)-BPS operators from supergravity, JHEP 04 (2017) 005 [arXiv:1701.00998] [INSPIRE].
G. Arutyunov, R. Klabbers and S. Savin, Four-point functions of 1/2-BPS operators of any weights in the supergravity approximation, JHEP 09 (2018) 118 [arXiv:1808.06788] [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].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
A.L. Fitzpatrick et al., A Natural Language for AdS/CFT Correlators, JHEP 11 (2011) 095 [arXiv:1107.1499] [INSPIRE].
L. Rastelli and X. Zhou, Mellin amplitudes for AdS5 × S5, Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].
L. Rastelli and X. Zhou, How to Succeed at Holographic Correlators Without Really Trying, JHEP 04 (2018) 014 [arXiv:1710.05923] [INSPIRE].
Z. Komargodski and A. Zhiboedov, Convexity and Liberation at Large Spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, The Analytic Bootstrap and AdS Superhorizon Locality, JHEP 12 (2013) 004 [arXiv:1212.3616] [INSPIRE].
L.F. Alday, Large Spin Perturbation Theory for Conformal Field Theories, Phys. Rev. Lett. 119 (2017) 111601 [arXiv:1611.01500] [INSPIRE].
S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].
D. Carmi and S. Caron-Huot, A Conformal Dispersion Relation: Correlations from Absorption, JHEP 09 (2020) 009 [arXiv:1910.12123] [INSPIRE].
D. Mazáč, L. Rastelli and X. Zhou, A basis of analytic functionals for CFTs in general dimension, JHEP 08 (2021) 140 [arXiv:1910.12855] [INSPIRE].
J. Penedones, J.A. Silva and A. Zhiboedov, Nonperturbative Mellin Amplitudes: Existence, Properties, Applications, JHEP 08 (2020) 031 [arXiv:1912.11100] [INSPIRE].
S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, Dispersive CFT Sum Rules, JHEP 05 (2021) 243 [arXiv:2008.04931] [INSPIRE].
A. Bissi, A. Sinha and X. Zhou, Selected topics in analytic conformal bootstrap: A guided journey, Phys. Rept. 991 (2022) 1 [arXiv:2202.08475] [INSPIRE].
O. Aharony, L.F. Alday, A. Bissi and E. Perlmutter, Loops in AdS from Conformal Field Theory, JHEP 07 (2017) 036 [arXiv:1612.03891] [INSPIRE].
L.F. Alday and A. Bissi, Loop Corrections to Supergravity on AdS5 × S5, 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].
L.F. Alday and S. Caron-Huot, Gravitational S-matrix from CFT dispersion relations, JHEP 12 (2018) 017 [arXiv:1711.02031] [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. 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].
L.F. Alday and X. Zhou, Simplicity of AdS Supergravity at One Loop, JHEP 09 (2020) 008 [arXiv:1912.02663] [INSPIRE].
E. D’Hoker, S.D. Mathur, A. Matusis and L. Rastelli, The Operator product expansion of N=4 SYM and the 4 point functions of supergravity, Nucl. Phys. B 589 (2000) 38 [hep-th/9911222] [INSPIRE].
G. Arutyunov and S. Frolov, Four point functions of lowest weight CPOs in N=4 SYM(4) in supergravity approximation, Phys. Rev. D 62 (2000) 064016 [hep-th/0002170] [INSPIRE].
R. Doobary and P. Heslop, Superconformal partial waves in Grassmannian field theories, JHEP 12 (2015) 159 [arXiv:1508.03611] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Unmixing Supergravity, JHEP 02 (2018) 133 [arXiv:1706.08456] [INSPIRE].
F. Aprile, J. 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].
A. Bissi, G. Fardelli and A. Georgoudis, All loop structures in supergravity amplitudes on AdS5 × S5 from CFT, J. Phys. A 54 (2021) 324002 [arXiv:2010.12557] [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. Chavez and C. Duhr, Three-mass triangle integrals and single-valued polylogarithms, JHEP 11 (2012) 114 [arXiv:1209.2722] [INSPIRE].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [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].
J. Maldacena, D. Simmons-Duffin and A. Zhiboedov, Looking for a bulk point, JHEP 01 (2017) 013 [arXiv:1509.03612] [INSPIRE].
D. Simmons-Duffin, D. Stanford and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, JHEP 07 (2018) 085 [arXiv:1711.03816] [INSPIRE].
L.F. Alday, A. Bissi and T. Lukowski, Lessons from crossing symmetry at large N, JHEP 06 (2015) 074 [arXiv:1410.4717] [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].
J.M. Drummond and H. Paul, One-loop string corrections to AdS amplitudes from CFT, JHEP 03 (2021) 038 [arXiv:1912.07632] [INSPIRE].
C. Duhr and F. Dulat, PolyLogTools — polylogs for the masses, JHEP 08 (2019) 135 [arXiv:1904.07279] [INSPIRE].
S.M. Chester, Genus-2 holographic correlator on AdS5 × S5 from localization, JHEP 04 (2020) 193 [arXiv:1908.05247] [INSPIRE].
S.M. Chester and S.S. Pufu, Far beyond the planar limit in strongly-coupled \( \mathcal{N} \) = 4 SYM, JHEP 01 (2021) 103 [arXiv:2003.08412] [INSPIRE].
L.F. Alday, J. Henriksson and M. van Loon, Taming the ϵ-expansion with large spin perturbation theory, JHEP 07 (2018) 131 [arXiv:1712.02314] [INSPIRE].
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Huang, Z., Yuan, E.Y. Graviton scattering in AdS5 × S5 at two loops. J. High Energ. Phys. 2023, 64 (2023). https://doi.org/10.1007/JHEP04(2023)064
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DOI: https://doi.org/10.1007/JHEP04(2023)064