Abstract
We consider the four-point function of the lowest scalar in the stress-energy tensor multiplet in \( \mathcal{N}=8 \) ABJ(M) theory [1, 2]. At large central charge cT ∼ N3/2, this correlator is given by the corresponding holographic correlation function in 11d supergravity on AdS4 × S7. We use Mellin space techniques to compute the leading 1/cT correction to anomalous dimensions and OPE coefficients of operators that appear in this holographic correlator. For half and quarter-BPS operators, we find exact agreement with previously computed localization results. For the other BPS and non-BPS operators, our results match the \( \mathcal{N}=8 \) numerical bootstrap for ABJ(M) at large cT, which provides a precise check of unprotected observables in AdS/CFT.
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References
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].
J. Bagger and N. Lambert, Comments on multiple M2-branes, JHEP 02 (2008) 105 [arXiv:0712.3738] [INSPIRE].
J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [INSPIRE].
J. Bagger and N. Lambert, Modeling Multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [INSPIRE].
A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [INSPIRE].
N. Lambert and C. Papageorgakis, Relating U(N) × U(N) to SU(N) × SU(N) Chern-Simons Membrane theories, JHEP 04 (2010) 104 [arXiv:1001.4779] [INSPIRE].
D. Bashkirov and A. Kapustin, Dualities between N = 8 superconformal field theories in three dimensions, JHEP 05 (2011) 074 [arXiv:1103.3548] [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].
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].
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].
S. Kim, The Complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [Erratum ibid. B 864 (2012) 884] [arXiv:0903.4172] [INSPIRE].
N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys. 306 (2011) 511 [arXiv:1007.3837] [INSPIRE].
C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Multi-Matrix Models and Tri-Sasaki Einstein Spaces, Phys. Rev. D 83 (2011) 046001 [arXiv:1011.5487] [INSPIRE].
S. Bhattacharyya, A. Grassi, M. Mariño and A. Sen, A One-Loop Test of Quantum Supergravity, Class. Quant. Grav. 31 (2014) 015012 [arXiv:1210.6057] [INSPIRE].
X. Zhou, On Superconformal Four-Point Mellin Amplitudes in Dimension d > 2, arXiv:1712.02800 [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].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [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].
L. Rastelli and X. Zhou, The Mellin Formalism for Boundary CFT d, JHEP 10 (2017) 146 [arXiv:1705.05362] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
M.F. Paulos, Towards Feynman rules for Mellin amplitudes, JHEP 10 (2011) 074 [arXiv:1107.1504] [INSPIRE].
D. Nandan, A. Volovich and C. Wen, On Feynman Rules for Mellin Amplitudes in AdS/CFT, JHEP 05 (2012) 129 [arXiv:1112.0305] [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].
E.Y. Yuan, Loops in the Bulk, arXiv:1710.01361 [INSPIRE].
C. Cardona, Mellin-(Schwinger) representation of One-loop Witten diagrams in AdS, arXiv:1708.06339 [INSPIRE].
L. Rastelli and X. Zhou, Mellin amplitudes for AdS 5 × S 5, Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].
R. Gopakumar, A. Kaviraj, K. Sen and A. Sinha, Conformal Bootstrap in Mellin Space, Phys. Rev. Lett. 118 (2017) 081601 [arXiv:1609.00572] [INSPIRE].
R. Gopakumar, A. Kaviraj, K. Sen and A. Sinha, A Mellin space approach to the conformal bootstrap, JHEP 05 (2017) 027 [arXiv:1611.08407] [INSPIRE].
V. Gonçalves, J. Penedones and E. Trevisani, Factorization of Mellin amplitudes, JHEP 10 (2015) 040 [arXiv:1410.4185] [INSPIRE].
A.A. Nizami, A. Rudra, S. Sarkar and M. Verma, Exploring Perturbative Conformal Field Theory in Mellin space, JHEP 01 (2017) 102 [arXiv:1607.07334] [INSPIRE].
M.F. Paulos, M. Spradlin and A. Volovich, Mellin Amplitudes for Dual Conformal Integrals, JHEP 08 (2012) 072 [arXiv:1203.6362] [INSPIRE].
L. Rastelli and X. Zhou, Holographic Four-Point Functions in the (2, 0) Theory, JHEP 06 (2018) 087 [arXiv:1712.02788] [INSPIRE].
L. Rastelli and X. Zhou, How to Succeed at Holographic Correlators Without Really Trying, JHEP 04 (2018) 014 [arXiv:1710.05923] [INSPIRE].
V. Gonçalves, Four point function of \( \mathcal{N}=4 \) stress-tensor multiplet at strong coupling, JHEP 04 (2015) 150 [arXiv:1411.1675] [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].
L.F. Alday, A. Bissi and T. Lukowski, Lessons from crossing symmetry at large N, JHEP 06 (2015) 074 [arXiv:1410.4717] [INSPIRE].
P. Heslop and A.E. Lipstein, M-theory Beyond The Supergravity Approximation, JHEP 02 (2018) 004 [arXiv:1712.08570] [INSPIRE].
M. Hogervorst, Dimensional Reduction for Conformal Blocks, JHEP 09 (2016) 017 [arXiv:1604.08913] [INSPIRE].
D. Simmons-Duffin, The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT, JHEP 03 (2017) 086 [arXiv:1612.08471] [INSPIRE].
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [INSPIRE].
T. Nosaka, Instanton effects in ABJM theory with general R-charge assignments, JHEP 03 (2016) 059 [arXiv:1512.02862] [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].
C. Beem, W. Peelaers and L. Rastelli, Deformation quantization and superconformal symmetry in three dimensions, Commun. Math. Phys. 354 (2017) 345 [arXiv:1601.05378] [INSPIRE].
C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli and B.C. van Rees, Infinite Chiral Symmetry in Four Dimensions, Commun. Math. Phys. 336 (2015) 1359 [arXiv:1312.5344] [INSPIRE].
M. Dedushenko, Y. Fan, S.S. Pufu and R. Yacoby, Coulomb Branch Operators and Mirror Symmetry in Three Dimensions, JHEP 04 (2018) 037 [arXiv:1712.09384] [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].
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 783 [hep-th/9712074] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and S. Raju, Indices for Superconformal Field Theories in 3,5 and 6 Dimensions, JHEP 02 (2008) 064 [arXiv:0801.1435] [INSPIRE].
F.A. Dolan, On Superconformal Characters and Partition Functions in Three Dimensions, J. Math. Phys. 51 (2010) 022301 [arXiv:0811.2740] [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].
F.A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [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, 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].
M. Hogervorst and S. Rychkov, Radial Coordinates for Conformal Blocks, Phys. Rev. D 87 (2013) 106004 [arXiv:1303.1111] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping the O(N) vector models, JHEP 06 (2014) 091 [arXiv:1307.6856] [INSPIRE].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
L.F. Alday and A. Bissi, Loop Corrections to Supergravity on AdS 5 × S 5, 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].
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Chester, S.M. AdS4/CFT3 for unprotected operators. J. High Energ. Phys. 2018, 30 (2018). https://doi.org/10.1007/JHEP07(2018)030
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DOI: https://doi.org/10.1007/JHEP07(2018)030