Abstract
We present a formula for the holographic 4-point correlators in AdS3 × S3 involving four single-trace operators of dimension k, k, l, l. As an input we use the super-gravity results for the Heavy-Heavy-Light-Light correlators that can be derived by studying the linear fluctuations around known asymptotically AdS3 × S3 geometries. When the operators of dimension k and l are in the same multiplet there are contributions due to the exchange of single-trace operators in the t and u-channels, which are not captured by the approach mentioned above. However by rewriting the s-channel results in Mellin space we obtain a compact expression for the s-channel contribution that makes it possible to conjecture a formula for the complete result. We discuss some consistency checks that our proposal meets.
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References
E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, hep-th/0201253 [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. 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, JHEP03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
L.F. Alday, Large Spin Perturbation Theory for Conformal Field Theories, Phys. Rev. Lett.119 (2017) 111601 [arXiv:1611.01500] [INSPIRE].
L.F. Alday and S. Caron-Huot, Gravitational S-matrix from CFT dispersion relations, JHEP12 (2018) 017 [arXiv:1711.02031] [INSPIRE].
S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP09 (2017) 078 [arXiv:1703.00278] [INSPIRE].
L. Rastelli and X. Zhou, Mellin amplitudes for AdS 5 × S 5, Phys. Rev. Lett.118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].
L. Rastelli and X. Zhou, How to Succeed at Holographic Correlators Without Really Trying, JHEP04 (2018) 014 [arXiv:1710.05923] [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].
S. Caron-Huot and A.-K. Trinh, All tree-level correlators in AdS 5 × S 5supergravity: hidden ten-dimensional conformal symmetry, JHEP01 (2019) 196 [arXiv:1809.09173] [INSPIRE].
X. Zhou, On Superconformal Four-Point Mellin Amplitudes in Dimension d > 2, JHEP08 (2018) 187 [arXiv:1712.02800] [INSPIRE].
L. Rastelli and X. Zhou, Holographic Four-Point Functions in the (2, 0) Theory, JHEP06 (2018) 087 [arXiv:1712.02788] [INSPIRE].
S.M. Chester and E. Perlmutter, M-Theory Reconstruction from (2, 0) CFT and the Chiral Algebra Conjecture, JHEP08 (2018) 116 [arXiv:1805.00892] [INSPIRE].
T. Abl, P. Heslop and A.E. Lipstein, Recursion relations for anomalous dimensions in the 6d (2, 0) theory, JHEP04 (2019) 038 [arXiv:1902.00463] [INSPIRE].
S.M. Chester, S.S. Pufu and X. Yin, The M-theory S-matrix From ABJM: Beyond 11D Supergravity, JHEP08 (2018) 115 [arXiv:1804.00949] [INSPIRE].
S.M. Chester, AdS 4/CFT 3for unprotected operators, JHEP07 (2018) 030 [arXiv:1803.01379] [INSPIRE].
D.J. Binder, S.M. Chester and S.S. Pufu, Absence of D 4R 4in M-theory From ABJM, arXiv:1808.10554 [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S. Giusto, R. Russo and C. Wen, Holographic correlators in AdS 3, JHEP03 (2019) 096 [arXiv:1812.06479] [INSPIRE].
O. Lunin and S.D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys.B 623 (2002) 342 [hep-th/0109154] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP06 (2007) 056 [arXiv:0704.0690] [INSPIRE].
A. Bombini, A. Galliani, S. Giusto, E. Moscato and R. Russo, Unitary 4-point correlators from classical geometries, Eur. Phys. J.C 78 (2018) 8 [arXiv:1710.06820] [INSPIRE].
A. Galliani, S. Giusto, E. Moscato and R. Russo, Correlators at large c without information loss, JHEP09 (2016) 065 [arXiv:1606.01119] [INSPIRE].
A. Galliani, S. Giusto and R. Russo, Holographic 4-point correlators with heavy states, JHEP10 (2017) 040 [arXiv:1705.09250] [INSPIRE].
A. Bombini and A. Galliani, AdS 3four-point functions from \( \frac{1}{8} \)-BPS states, JHEP06 (2019) 044 [arXiv:1904.02656] [INSPIRE].
J. Tian, J. Hou and B. Chen, Holographic Correlators on Integrable Superstrata, arXiv:1904.04532 [INSPIRE].
I. Bena, P. Heidmann, R. Monten and N.P. Warner, Thermal Decay without Information Loss in Horizonless Microstate Geometries, arXiv:1905.05194 [INSPIRE].
S. Giusto, R. Russo, A. Tyukov and C. Wen, General AdS_3/CFT_2 correlators from supergravity, in progress.
L. Rastelli, K. Roumpedakis and X. Zhou, AdS 3 × S 3Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry, arXiv:1905.11983 [INSPIRE].
I. Bena, S. Giusto, R. Russo, M. Shigemori and N.P. Warner, Habemus Superstratum! A constructive proof of the existence of superstrata, JHEP05 (2015) 110 [arXiv:1503.01463] [INSPIRE].
G. Arutyunov and S. Frolov, On the correspondence between gravity fields and CFT operators, JHEP04 (2000) 017 [hep-th/0003038] [INSPIRE].
M. Heydeman, J.H. Schwarz, C. Wen and S.-Q. Zhang, All Tree Amplitudes of 6D (2, 0) Supergravity: Interacting Tensor Multiplets and the K3 Moduli Space, Phys. Rev. Lett.122 (2019) 111604 [arXiv:1812.06111] [INSPIRE].
R.H. Boels and D. O’Connell, Simple superamplitudes in higher dimensions, JHEP06 (2012) 163 [arXiv:1201.2653] [INSPIRE].
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ArXiv ePrint: 1905.12314
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Giusto, S., Russo, R., Tyukov, A. et al. Holographic correlators in AdS3 without Witten diagrams. J. High Energ. Phys. 2019, 30 (2019). https://doi.org/10.1007/JHEP09(2019)030
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DOI: https://doi.org/10.1007/JHEP09(2019)030