Abstract
We study four-point functions of arbitrary half-BPS operators in a 4-dimensional \( \mathcal{N} \) = 2 SCFT with flavour group SO(8) at genus-zero and strong ’t Hooft coupling, corresponding — via AdS/CFT — to the (α′ expansion of the) Veneziano amplitude on an AdS5×S3 background. We adapt a procedure first proposed by Abl, Heslop and Lipstein in the context of AdS5×S5, and postulate the existence of an effective action in terms of an 8-dimensional scalar field valued in the adjoint of the flavour group. The various Kaluza-Klein correlators can then be computed by uplifting the standard AdS/CFT prescription to the full product geometry with AdS bulk-to-boundary propagators and Witten diagrams replaced by suitable AdS5×S3 versions. After elucidating the main features of the procedure, valid at all orders in α′, we show explicit results up to order α′5. The results provide further evidence of a novel relation between AdS×S and flat amplitudes — which made its first appearance in \( \mathcal{N} \) = 4 SYM — that is perhaps the most natural extension of the well known flat-space limit proposed by Penedones to cases where AdS and S have the same radius.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
L. Rastelli and X. Zhou, How to Succeed at Holographic Correlators Without Really Trying, JHEP 04 (2018) 014 [arXiv:1710.05923] [INSPIRE].
L. Rastelli and X. Zhou, Mellin amplitudes for AdS5 × S5, Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [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, JHEP 04 (2021) 005 [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].
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, Quantum Gravity from Conformal Field Theory, JHEP 01 (2018) 035 [arXiv:1706.02822] [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].
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 and H. Paul, One-loop string corrections to AdS amplitudes from CFT, JHEP 03 (2021) 038 [arXiv:1912.07632] [INSPIRE].
V. Gonçalves, Four point function of \( \mathcal{N} \) = 4 stress-tensor multiplet at strong coupling, JHEP 04 (2015) 150 [arXiv:1411.1675] [INSPIRE].
J.M. Drummond, H. Paul and M. Santagata, Bootstrapping string theory on AdS5 × S5, arXiv:2004.07282 [INSPIRE].
F. Aprile, J.M. Drummond, H. Paul and M. Santagata, The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry, JHEP 11 (2021) 109 [arXiv:2012.12092] [INSPIRE].
A. Bissi, G. Fardelli and A. Georgoudis, Towards all loop supergravity amplitudes on AdS5×S5, Phys. Rev. D 104 (2021) L041901 [arXiv:2002.04604] [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].
F. Aprile and P. Vieira, Large p explorations. From SUGRA to big STRINGS in Mellin space, JHEP 12 (2020) 206 [arXiv:2007.09176] [INSPIRE].
J.M. Drummond, R. Glew and H. Paul, One-loop string corrections for AdS Kaluza-Klein amplitudes, JHEP 12 (2021) 072 [arXiv:2008.01109] [INSPIRE].
F. Aprile, J.M. Drummond, R. Glew and M. Santagata, One-loop string amplitudes in AdS5×S5: Mellin space and sphere splitting, JHEP 02 (2023) 087 [arXiv:2207.13084] [INSPIRE].
Z. Huang and E.Y. Yuan, Graviton scattering in AdS5 × S5 at two loops, JHEP 04 (2023) 064 [arXiv:2112.15174] [INSPIRE].
J.M. Drummond and H. Paul, Two-loop supergravity on AdS5×S5 from CFT, JHEP 08 (2022) 275 [arXiv:2204.01829] [INSPIRE].
L.F. Alday, T. Hansen and J.A. Silva, AdS Virasoro-Shapiro from dispersive sum rules, JHEP 10 (2022) 036 [arXiv:2204.07542] [INSPIRE].
L.F. Alday, T. Hansen and J.A. Silva, AdS Virasoro-Shapiro from single-valued periods, JHEP 12 (2022) 010 [arXiv:2209.06223] [INSPIRE].
P. Heslop, The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators, J. Phys. A 55 (2022) 443009 [arXiv:2203.13019] [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].
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].
S. Caron-Huot and F. Coronado, Ten dimensional symmetry of \( \mathcal{N} \) = 4 SYM correlators, JHEP 03 (2022) 151 [arXiv:2106.03892] [INSPIRE].
S. Caron-Huot, F. Coronado and B. Mühlmann, Determinants in self-dual N=4 SYM and twistor space, arXiv:2304.12341 [INSPIRE].
T. Abl, P. Heslop and A.E. Lipstein, Towards the Virasoro-Shapiro amplitude in AdS5 × S5, JHEP 04 (2021) 237 [arXiv:2012.12091] [INSPIRE].
T. Abl, P. Heslop and A.E. Lipstein, Higher-dimensional symmetry of AdS2×S2 correlators, JHEP 03 (2022) 076 [arXiv:2112.09597] [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].
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, The CFT6 origin of all tree-level 4-point correlators in AdS3 × S3, Eur. Phys. J. C 80 (2020) 736 [arXiv:2005.08560] [INSPIRE].
A. Sen, F theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
A. Fayyazuddin and M. Spalinski, Large N superconformal gauge theories and supergravity orientifolds, Nucl. Phys. B 535 (1998) 219 [hep-th/9805096] [INSPIRE].
O. Aharony, A. Fayyazuddin and J.M. Maldacena, The Large N limit of N=2, N=1 field theories from three-branes in F theory, JHEP 07 (1998) 013 [hep-th/9806159] [INSPIRE].
L.F. Alday, C. Behan, P. Ferrero and X. Zhou, Gluon Scattering in AdS from CFT, JHEP 06 (2021) 020 [arXiv:2103.15830] [INSPIRE].
L.F. Alday, A. Bissi and X. Zhou, One-loop gluon amplitudes in AdS, JHEP 02 (2022) 105 [arXiv:2110.09861] [INSPIRE].
Z. Huang, B. Wang, E.Y. Yuan and X. Zhou, AdS super gluon scattering up to two loops: a position space approach, JHEP 07 (2023) 053 [arXiv:2301.13240] [INSPIRE].
J.M. Drummond, R. Glew and M. Santagata, Bern-Carrasco-Johansson relations in AdS5×S3 and the double-trace spectrum of super gluons, Phys. Rev. D 107 (2023) L081901 [arXiv:2202.09837] [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].
C. Behan, S.M. Chester and P. Ferrero, Gluon scattering in AdS at finite string coupling from localization, arXiv:2305.01016 [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS / CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
M. Nirschl and H. Osborn, Superconformal Ward identities and their solution, Nucl. Phys. B 711 (2005) 409 [hep-th/0407060] [INSPIRE].
O. Schlotterer and S. Stieberger, Motivic Multiple Zeta Values and Superstring Amplitudes, J. Phys. A 46 (2013) 475401 [arXiv:1205.1516] [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. Stieberger, Open & Closed vs. Pure Open String Disk Amplitudes, arXiv:0907.2211 [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
C. Sleight, Interactions in Higher-Spin Gravity: a Holographic Perspective, J. Phys. A 50 (2017) 383001 [arXiv:1610.01318] [INSPIRE].
H.-Y. Chen and J.-I. Sakamoto, Superconformal Block from Holographic Geometry, JHEP 07 (2020) 028 [arXiv:2003.13343] [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].
M. Santagata, Holographic correlators and their (hidden) symmetries, Ph.D. thesis, University of Southampton, Southampton (2022) [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 and S.S. Pufu, Far beyond the planar limit in strongly-coupled \( \mathcal{N} \) = 4 SYM, JHEP 01 (2021) 103 [arXiv:2003.08412] [INSPIRE].
S.M. Chester et al., New modular invariants in \( \mathcal{N} \) = 4 Super-Yang-Mills theory, JHEP 04 (2021) 212 [arXiv:2008.02713] [INSPIRE].
F. Aprile and M. Santagata, Two particle spectrum of tensor multiplets coupled to AdS3×S3 gravity, Phys. Rev. D 104 (2021) 126022 [arXiv:2104.00036] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
X. Zhou, Double Copy Relation in AdS Space, Phys. Rev. Lett. 127 (2021) 141601 [arXiv:2106.07651] [INSPIRE].
J.A. Farrow, A.E. Lipstein and P. McFadden, Double copy structure of CFT correlators, JHEP 02 (2019) 130 [arXiv:1812.11129] [INSPIRE].
A.E. Lipstein and P. McFadden, Double copy structure and the flat space limit of conformal correlators in even dimensions, Phys. Rev. D 101 (2020) 125006 [arXiv:1912.10046] [INSPIRE].
C. Armstrong, A.E. Lipstein and J. Mei, Color/kinematics duality in AdS4, JHEP 02 (2021) 194 [arXiv:2012.02059] [INSPIRE].
S. Albayrak, S. Kharel and D. Meltzer, On duality of color and kinematics in (A)dS momentum space, JHEP 03 (2021) 249 [arXiv:2012.10460] [INSPIRE].
C. Cheung, J. Parra-Martinez and A. Sivaramakrishnan, On-shell correlators and color-kinematics duality in curved symmetric spacetimes, JHEP 05 (2022) 027 [arXiv:2201.05147] [INSPIRE].
A. Herderschee, R. Roiban and F. Teng, On the differential representation and color-kinematics duality of AdS boundary correlators, JHEP 05 (2022) 026 [arXiv:2201.05067] [INSPIRE].
A. Lipstein and S. Nagy, Self-dual gravity and color/kinematics duality in AdS4, arXiv:2304.07141 [INSPIRE].
C. Armstrong, H. Goodhew, A. Lipstein and J. Mei, Graviton Trispectrum from Gluons, arXiv:2304.07206 [INSPIRE].
Acknowledgments
We thank James Drummond, Pietro Ferrero, Paul Heslop, Arthur Lipstein for providing important comment and feedback on the manuscript, James Drummond for collaboration at early stage of this project, Heng-Yu Chen and Yu-tin Huang for discussion on related topics. MS is supported by Ministry of Science and Technology (MOST) through the grant 110-2112-M-002-006-. RG is supported by the Mathematics and Theoretical Physics research group at the University of Hertfordshire.
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: 2305.01013
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
Glew, R., Santagata, M. The Veneziano amplitude in AdS5×S3 from an 8-dimensional effective action. J. High Energ. Phys. 2023, 10 (2023). https://doi.org/10.1007/JHEP08(2023)010
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)010