Abstract
We study the stress tensor multiplet four-point function in the 3d maximally supersymmetric ABJ(M) theory with Chern-Simons level k = 2, which in the large N limit is holographically dual to weakly coupled M-theory on AdS4 × S7/ℤ2. We use the Lorentzian inversion to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity R and the first higher derivative correction R4 vertices, up to a finite number of contact terms that contribute to low spins where the inversion formula does not converge. We find a precise match with the corresponding terms in the 11d M-theory S-matrix by taking the flat space limit, which is not sensitive to these contact terms. We then conjecturally fix these contact terms by analytically continuing the inversion formula below its expected range of convergence, and verify this conjecture using supersymmetric localization. Finally, we compare some of the 1-loop CFT data to non-perturbative in N bounds from the numerical conformal bootstrap, which we compute at unprecedently high accuracy, and find that the 1-loop corrections saturate the bounds in the large N regime, which extends the previously observed match at tree level.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].
L. Susskind, Holography in the flat space limit, AIP Conf. Proc. 493 (1999) 98 [hep-th/9901079] [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].
A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Scattering States in AdS/CFT, arXiv:1104.2597 [INSPIRE].
M.B. Green, M. Gutperle and P. Vanhove, One loop in eleven-dimensions, Phys. Lett. B 409 (1997) 177 [hep-th/9706175] [INSPIRE].
J.G. Russo and A.A. Tseytlin, One loop four graviton amplitude in eleven-dimensional supergravity, Nucl. Phys. B 508 (1997) 245 [hep-th/9707134] [INSPIRE].
M.B. Green and P. Vanhove, Duality and higher derivative terms in M-theory, JHEP 01 (2006) 093 [hep-th/0510027] [INSPIRE].
S.M. Chester, S.S. Pufu and X. Yin, The M-theory S-matrix From ABJM: Beyond 11D Supergravity, JHEP 08 (2018) 115 [arXiv:1804.00949] [INSPIRE].
G. Arutyunov and S. Frolov, Four point functions of lowest weight CPOs in N = 4 SYM4 in supergravity approximation, Phys. Rev. D 62 (2000) 064016 [hep-th/0002170] [INSPIRE].
G. Arutyunov and E. Sokatchev, Implications of superconformal symmetry for interacting (2, 0) tensor multiplets, Nucl. Phys. B 635 (2002) 3 [hep-th/0201145] [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].
E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton and gauge boson propagators in AdSd+1, Nucl. Phys. B 562 (1999) 330 [hep-th/9902042] [INSPIRE].
E. D’Hoker, D.Z. Freedman and L. Rastelli, AdS/CFT four point functions: How to succeed at z integrals without really trying, Nucl. Phys. B 562 (1999) 395 [hep-th/9905049] [INSPIRE].
E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton exchange and complete four point functions in the AdS/CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th/9903196] [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].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
D.J. Binder, S.M. Chester and S.S. Pufu, Absence of D4R4 in M-theory From ABJM, JHEP 04 (2020) 052 [arXiv:1808.10554] [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].
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].
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, JHEP 01 (2021) 103 [arXiv:2003.08412] [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].
S.M. Chester, Genus-2 holographic correlator on AdS5 × S5 from localization, JHEP 04 (2020) 193 [arXiv:1908.05247] [INSPIRE].
S.M. Chester and E. Perlmutter, M-Theory Reconstruction from (2, 0) CFT and the Chiral Algebra Conjecture, JHEP 08 (2018) 116 [arXiv:1805.00892] [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].
S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [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].
M. Lemos, B.C. van Rees and X. Zhao, Regge trajectories for the (2, 0) theories, JHEP 01 (2022) 022 [arXiv:2105.13361] [INSPIRE].
L.F. Alday and A. Bissi, Loop Corrections to Supergravity on AdS5 × S5, Phys. Rev. Lett. 119 (2017) 171601 [arXiv:1706.02388] [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].
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, Quantum Gravity from Conformal Field Theory, JHEP 01 (2018) 035 [arXiv:1706.02822] [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, 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 and H. Paul, One-loop string corrections to AdS amplitudes from CFT, JHEP 03 (2021) 038 [arXiv:1912.07632] [INSPIRE].
J.M. Drummond, H. Paul and M. Santagata, Bootstrapping string theory on AdS5 × S5, arXiv:2004.07282 [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].
L.F. Alday, S.M. Chester and H. Raj, 6d (2, 0) and M-theory at 1-loop, JHEP 01 (2021) 133 [arXiv:2005.07175] [INSPIRE].
O. Aharony, L.F. Alday, A. Bissi and R. Yacoby, The Analytic Bootstrap for Large N Chern-Simons Vector Models, JHEP 08 (2018) 166 [arXiv:1805.04377] [INSPIRE].
D.J. Binder, S.M. Chester and M. Jerdee, ABJ Correlators with Weakly Broken Higher Spin Symmetry, JHEP 04 (2021) 242 [arXiv:2103.01969] [INSPIRE].
G.J. Turiaci and A. Zhiboedov, Veneziano Amplitude of Vasiliev Theory, JHEP 10 (2018) 034 [arXiv:1802.04390] [INSPIRE].
Z. Li, Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization, JHEP 10 (2020) 007 [arXiv:1906.05834] [INSPIRE].
J.A. Silva, Four point functions in CFT’s with slightly broken higher spin symmetry, JHEP 05 (2021) 097 [arXiv:2103.00275] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
S.M. Chester, J. Lee, S.S. Pufu and R. Yacoby, The \( \mathcal{N} \) = 8 superconformal bootstrap in three dimensions, JHEP 09 (2014) 143 [arXiv:1406.4814] [INSPIRE].
D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories, JHEP 10 (2012) 053 [arXiv:1205.4142] [INSPIRE].
X. Zhou, On Superconformal Four-Point Mellin Amplitudes in Dimension d > 2, JHEP 08 (2018) 187 [arXiv:1712.02800] [INSPIRE].
F.A. Dolan, L. Gallot and E. Sokatchev, On four-point functions of 1/2-BPS operators in general dimensions, JHEP 09 (2004) 056 [hep-th/0405180] [INSPIRE].
L.F. Alday and X. Zhou, All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs, Phys. Rev. X 11 (2021) 011056 [arXiv:2006.12505] [INSPIRE].
N.B. Agmon, S.M. Chester and S.S. Pufu, Solving M-theory with the Conformal Bootstrap, JHEP 06 (2018) 159 [arXiv:1711.07343] [INSPIRE].
T. Nosaka, Instanton effects in ABJM theory with general R-charge assignments, JHEP 03 (2016) 059 [arXiv:1512.02862] [INSPIRE].
M. Dedushenko, S.S. Pufu and R. Yacoby, A one-dimensional theory for Higgs branch operators, JHEP 03 (2018) 138 [arXiv:1610.00740] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
S.M. Chester, AdS4/CFT3 for unprotected operators, JHEP 07 (2018) 030 [arXiv:1803.01379] [INSPIRE].
S.M. Chester, J. Lee, S.S. Pufu and R. Yacoby, Exact Correlators of BPS Operators from the 3d Superconformal Bootstrap, JHEP 03 (2015) 130 [arXiv:1412.0334] [INSPIRE].
N.B. Agmon, S.M. Chester and S.S. Pufu, The M-theory Archipelago, JHEP 02 (2020) 010 [arXiv:1907.13222] [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, More \( \mathcal{N} \) = 4 superconformal bootstrap, Phys. Rev. D 96 (2017) 046014 [arXiv:1612.02363] [INSPIRE].
C. Beem, M. Lemos, L. Rastelli and B.C. van Rees, The (2, 0) superconformal bootstrap, Phys. Rev. D 93 (2016) 025016 [arXiv:1507.05637] [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].
M. Nirschl and H. Osborn, Superconformal Ward identities and their solution, Nucl. Phys. B 711 (2005) 409 [hep-th/0407060] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal Partial Waves: Further Mathematical Results, arXiv:1108.6194 [INSPIRE].
F.A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping the O(N) vector models, JHEP 06 (2014) 091 [arXiv:1307.6856] [INSPIRE].
S. Ferrara and E. Sokatchev, Universal properties of superconformal OPEs for 1/2 BPS operators in 3 ≤ d ≤ 6, New J. Phys. 4 (2002) 2 [hep-th/0110174] [INSPIRE].
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions, JHEP 03 (2019) 163 [arXiv:1612.00809] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].
D. Gaiotto and J. Abajian, Twisted M2 brane holography and sphere correlation functions, arXiv:2004.13810 [INSPIRE].
L.F. Alday, Large Spin Perturbation Theory for Conformal Field Theories, Phys. Rev. Lett. 119 (2017) 111601 [arXiv:1611.01500] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Unmixing Supergravity, JHEP 02 (2018) 133 [arXiv:1706.08456] [INSPIRE].
Z. Komargodski and A. Zhiboedov, Convexity and Liberation at Large Spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].
W. Landry and D. Simmons-Duffin, Scaling the semidefinite program solver SDPB, arXiv:1909.09745 [INSPIRE].
D. Simmons-Duffin, A Semidefinite Program Solver for the Conformal Bootstrap, JHEP 06 (2015) 174 [arXiv:1502.02033] [INSPIRE].
D. Gang, E. Koh, K. Lee and J. Park, ABCD of 3d \( \mathcal{N} \) = 8 and 4 Superconformal Field Theories, arXiv:1108.3647 [INSPIRE].
N.B. Agmon, S.M. Chester and S.S. Pufu, A new duality between \( \mathcal{N} \) = 8 superconformal field theories in three dimensions, JHEP 06 (2018) 005 [arXiv:1708.07861] [INSPIRE].
S.M. Chester, R.R. Kalloor and A. Sharon, Squashing, Mass, and Holography for 3d Sphere Free Energy, JHEP 04 (2021) 244 [arXiv:2102.05643] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, SUSY Gauge Theories on Squashed Three-Spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].
Y. Imamura and D. Yokoyama, N = 2 supersymmetric theories on squashed three-sphere, Phys. Rev. D 85 (2012) 025015 [arXiv:1109.4734] [INSPIRE].
F.A. Dolan, On Superconformal Characters and Partition Functions in Three Dimensions, J. Math. Phys. 51 (2010) 022301 [arXiv:0811.2740] [INSPIRE].
W. Li, Lightcone expansions of conformal blocks in closed form, JHEP 06 (2020) 105 [arXiv:1912.01168] [INSPIRE].
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: 2107.10274
Supplementary Information
ESM 1
(TGZ 516 kb)
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. & Raj, H. ABJM at strong coupling from M-theory, localization, and Lorentzian inversion. J. High Energ. Phys. 2022, 5 (2022). https://doi.org/10.1007/JHEP02(2022)005
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2022)005