Abstract
We compute the AdS Veneziano amplitude for type IIB gluon scattering in AdS5 × S3 to all orders in α′ in a small curvature expansion. This is achieved by combining a dispersion relation in the dual 4d \( \mathcal{N} \) = 2 SCFT with an ansatz for the amplitude as a worldsheet integral in terms of multiple polylogarithms. The first curvature correction is fully fixed in this way and satisfies consistency checks in the high energy limit, the low energy expansion as previously fixed using supersymmetric localisation, and for the energy of massive string operators, which we independently compute using a semiclassical expansion. We also combine localisation with this first curvature correction to fix the unprotected D4F4 correction to the amplitude at finite curvature.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge University Press (2007) [https://doi.org/10.1017/CBO9780511618123] [INSPIRE].
M.B. Green and J.H. Schwarz, Supersymmetrical Dual String Theory, Nucl. Phys. B 181 (1981) 502 [INSPIRE].
N. Berkovits, Super Poincare covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035] [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, A. Bissi and T. Lukowski, Lessons from crossing symmetry at large N, JHEP 06 (2015) 074 [arXiv:1410.4717] [INSPIRE].
V. Gonçalves, Four point function of \( \mathcal{N} \) = 4 stress-tensor multiplet at strong coupling, JHEP 04 (2015) 150 [arXiv:1411.1675] [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].
A.L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju and B.C. van Rees, A Natural Language for AdS/CFT Correlators, JHEP 11 (2011) 095 [arXiv:1107.1499] [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 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, 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, M.B. Green, S.S. Pufu, Y. Wang and C. Wen, New modular invariants in \( \mathcal{N} \) = 4 Super-Yang-Mills theory, JHEP 04 (2021) 212 [arXiv:2008.02713] [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [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].
L.F. Alday, T. Hansen and J.A. Silva, Emergent Worldsheet for the AdS Virasoro-Shapiro Amplitude, Phys. Rev. Lett. 131 (2023) 161603 [arXiv:2305.03593] [INSPIRE].
L.F. Alday and T. Hansen, The AdS Virasoro-Shapiro amplitude, JHEP 10 (2023) 023 [arXiv:2306.12786] [INSPIRE].
N. Gromov, D. Serban, I. Shenderovich and D. Volin, Quantum folded string and integrability: From finite size effects to Konishi dimension, JHEP 08 (2011) 046 [arXiv:1102.1040] [INSPIRE].
A. Sen, F theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
T. Banks, M.R. Douglas and N. Seiberg, Probing F theory with branes, Phys. Lett. B 387 (1996) 278 [hep-th/9605199] [INSPIRE].
M.R. Douglas, D.A. Lowe and J.H. Schwarz, Probing F theory with multiple branes, Phys. Lett. B 394 (1997) 297 [hep-th/9612062] [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].
I.P. Ennes, C. Lozano, S.G. Naculich and H.J. Schnitzer, Elliptic models, type IIB orientifolds and the AdS / CFT correspondence, Nucl. Phys. B 591 (2000) 195 [hep-th/0006140] [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].
C. Behan, S.M. Chester and P. Ferrero, Gluon scattering in AdS at finite string coupling from localization, JHEP 02 (2024) 042 [arXiv:2305.01016] [INSPIRE].
L.F. Alday, T. Hansen and M. Nocchi, High Energy String Scattering in AdS, JHEP 02 (2024) 089 [arXiv:2312.02261] [INSPIRE].
D.J. Gross and J.L. Manes, The High-energy Behavior of Open String Scattering, Nucl. Phys. B 326 (1989) 73 [INSPIRE].
B. Chen, X.-J. Wang and Y.-S. Wu, Integrable open spin chain in superYang-Mills and the plane wave/SYM duality, JHEP 02 (2004) 029 [hep-th/0401016] [INSPIRE].
B. Chen, X.-J. Wang and Y.-S. Wu, Open spin chain and open spinning string, Phys. Lett. B 591 (2004) 170 [hep-th/0403004] [INSPIRE].
B. Stefanski Jr., Open spinning strings, JHEP 03 (2004) 057 [hep-th/0312091] [INSPIRE].
D.E. Berenstein, E. Gava, J.M. Maldacena, K.S. Narain and H.S. Nastase, Open strings on plane waves and their Yang-Mills duals, hep-th/0203249 [INSPIRE].
R. Roiban and A.A. Tseytlin, Semiclassical string computation of strong-coupling corrections to dimensions of operators in Konishi multiplet, Nucl. Phys. B 848 (2011) 251 [arXiv:1102.1209] [INSPIRE].
F.A. Dolan and H. Osborn, Superconformal symmetry, correlation functions and the operator product expansion, Nucl. Phys. B 629 (2002) 3 [hep-th/0112251] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-Matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
J. Penedones, J.A. Silva and A. Zhiboedov, Nonperturbative Mellin Amplitudes: Existence, Properties, Applications, JHEP 08 (2020) 031 [arXiv:1912.11100] [INSPIRE].
G. Fardelli, T. Hansen and J.A. Silva, AdS Virasoro-Shapiro amplitude with KK modes, JHEP 11 (2023) 064 [arXiv:2308.03683] [INSPIRE].
R. Roiban and A.A. Tseytlin, Quantum strings in AdS5 × S5: Strong-coupling corrections to dimension of Konishi operator, JHEP 11 (2009) 013 [arXiv:0906.4294] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions, JHEP 03 (2019) 163 [arXiv:1612.00809] [INSPIRE].
N. Mann and S.E. Vazquez, Classical Open String Integrability, JHEP 04 (2007) 065 [hep-th/0612038] [INSPIRE].
A. Dekel and Y. Oz, Integrability of Green-Schwarz Sigma Models with Boundaries, JHEP 08 (2011) 004 [arXiv:1106.3446] [INSPIRE].
G. Linardopoulos and K. Zarembo, String integrability of defect CFT and dynamical reflection matrices, JHEP 05 (2021) 203 [arXiv:2102.12381] [INSPIRE].
G. Linardopoulos, String integrability of the ABJM defect, JHEP 06 (2022) 033 [arXiv:2202.06824] [INSPIRE].
F.A. Dolan and H. Osborn, On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys. 307 (2003) 41 [hep-th/0209056] [INSPIRE].
E.G. Gimon and J. Polchinski, Consistency conditions for orientifolds and D-manifolds, Phys. Rev. D 54 (1996) 1667 [hep-th/9601038] [INSPIRE].
K. Okamura, Y. Takayama and K. Yoshida, Open spinning strings and AdS/dCFT duality, JHEP 01 (2006) 112 [hep-th/0511139] [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].
M. Beccaria, G.V. Dunne and A.A. Tseytlin, Strong coupling expansion of free energy and BPS Wilson loop in \( \mathcal{N} \) = 2 superconformal models with fundamental hypermultiplets, JHEP 08 (2021) 102 [arXiv:2105.14729] [INSPIRE].
M. Beccaria, G.P. Korchemsky and A.A. Tseytlin, Exact strong coupling results in \( \mathcal{N} \) = 2 Sp(2N) superconformal gauge theory from localization, JHEP 01 (2023) 037 arXiv:2210.13871] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, \( \mathcal{N} \) = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
A. Cavaglià, D. Fioravanti, N. Gromov and R. Tateo, Quantum Spectral Curve of the \( \mathcal{N} \) = 6 Supersymmetric Chern-Simons Theory, Phys. Rev. Lett. 113 (2014) 021601 [arXiv:1403.1859] [INSPIRE].
D.J. Binder, S.M. Chester and S.S. Pufu, AdS4/CFT3 from weak to strong string coupling, JHEP 01 (2020) 034 [arXiv:1906.07195] [INSPIRE].
D.J. Binder, S.M. Chester, M. Jerdee and S.S. Pufu, The 3d \( \mathcal{N} \) = 6 bootstrap: from higher spins to strings to membranes, JHEP 05 (2021) 083 [arXiv:2011.05728] [INSPIRE].
P. Dey, K. Ghosh and A. Sinha, Simplifying large spin bootstrap in Mellin space, JHEP 01 (2018) 152 [arXiv:1709.06110] [INSPIRE].
S.M. Chester, Bootstrapping 4d \( \mathcal{N} \) = 2 gauge theories: the case of SQCD, JHEP 01 (2023) 107 [arXiv:2205.12978] [INSPIRE].
P. Vanhove and F. Zerbini, Single-valued hyperlogarithms, correlation functions and closed string amplitudes, Adv. Theor. Math. Phys. 26 (2022) 455 [arXiv:1812.03018] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A Semiclassical limit of the gauge / string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
J.A. Minahan, Circular semiclassical string solutions on AdS5 × S5, Nucl. Phys. B 648 (2003) 203 [hep-th/0209047] [INSPIRE].
S. Frolov and A.A. Tseytlin, Semiclassical quantization of rotating superstring in AdS5 × S5, JHEP 06 (2002) 007 [hep-th/0204226] [INSPIRE].
S. Frolov and A.A. Tseytlin, Multispin string solutions in AdS5 × S5, Nucl. Phys. B 668 (2003) 77 [hep-th/0304255] [INSPIRE].
S. Frolov and A.A. Tseytlin, Quantizing three spin string solution in AdS5 × S5, JHEP 07 (2003) 016 [hep-th/0306130] [INSPIRE].
G. Arutyunov, J. Russo and A.A. Tseytlin, Spinning strings in AdS5 × S5: New integrable system relations, Phys. Rev. D 69 (2004) 086009 [hep-th/0311004] [INSPIRE].
N. Beisert, S. Frolov, M. Staudacher and A.A. Tseytlin, Precision spectroscopy of AdS/CFT, JHEP 10 (2003) 037 [hep-th/0308117] [INSPIRE].
A. Tirziu and A.A. Tseytlin, Quantum corrections to energy of short spinning string in AdS5, Phys. Rev. D 78 (2008) 066002 [arXiv:0806.4758] [INSPIRE].
M. Beccaria and A. Tirziu, On the short string limit of the folded spinning string in AdS5 × S5, arXiv:0810.4127 [INSPIRE].
S. Frolov and A.A. Tseytlin, Rotating string solutions: AdS/CFT duality in nonsupersymmetric sectors, Phys. Lett. B 570 (2003) 96 [hep-th/0306143] [INSPIRE].
A.A. Tseytlin, Semiclassical strings and AdS/CFT, in the proceedings of the NATO Advanced Study Institute and EC Summer School on String Theory: From Gauge Interactions to Cosmology, Cargese, France (2004), pg. 265 [hep-th/0409296] [INSPIRE].
A.A. Tseytlin, Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions, Lett. Math. Phys. 99 (2012) 103 [arXiv:1012.3986] [INSPIRE].
L.J. Dixon, C. Duhr and J. Pennington, Single-valued harmonic polylogarithms and the multi-Regge limit, JHEP 10 (2012) 074 [arXiv:1207.0186] [INSPIRE].
Acknowledgments
We thank Connor Behan, Joao Silva, Bogdan Stefanski and Arkady Tseytlin for useful conversations. The work of LFA and TH is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 787185). LFA is also supported in part by the STFC grant ST/T000864/1. TH is also supported by the STFC grant ST/X000591/1. SMC and DlZ are supported by the Royal Society under the grant URF\R1\221310.
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: 2403.13877
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
Alday, L.F., Chester, S.M., Hansen, T. et al. The AdS Veneziano amplitude at small curvature. J. High Energ. Phys. 2024, 322 (2024). https://doi.org/10.1007/JHEP05(2024)322
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2024)322