Abstract
We compute the tree-level connected six-point function of identical scalar fluctuations of the AdS2 string worldsheet dual to the half-BPS Wilson line in planar \( \mathcal{N} \) = 4 Super Yang-Mills. The calculation can be carried out analytically in the conformal gauge approach, where the boundary reparametrization mode of the string plays a crucial role. We also study the analytic continuation of the six-point function to an out-of-time-order configuration, which is related to a 3-to-3 scattering amplitude in flat space. As a check of our results, we also numerically compute the six-point function using the Nambu-Goto action in static gauge, finding agreement with the conformal gauge answer.
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F.M. Haehl and M. Rozali, Fine Grained Chaos in AdS2 Gravity, Phys. Rev. Lett. 120 (2018) 121601 [arXiv:1712.04963] [INSPIRE].
F.M. Haehl, R. Loganayagam, P. Narayan and M. Rangamani, Classification of out-of-time-order correlators, SciPost Phys. 6 (2019) 001 [arXiv:1701.02820] [INSPIRE].
F.M. Haehl, A. Streicher and Y. Zhao, Six-point functions and collisions in the black hole interior, JHEP 08 (2021) 134 [arXiv:2105.12755] [INSPIRE].
V. Rosenhaus, Multipoint Conformal Blocks in the Comb Channel, JHEP 02 (2019) 142 [arXiv:1810.03244] [INSPIRE].
J.-F. Fortin, W. Ma and W. Skiba, Higher-Point Conformal Blocks in the Comb Channel, JHEP 07 (2020) 213 [arXiv:1911.11046] [INSPIRE].
J.-F. Fortin, W.-J. Ma and W. Skiba, Seven-point conformal blocks in the extended snowflake channel and beyond, Phys. Rev. D 102 (2020) 125007 [arXiv:2006.13964] [INSPIRE].
J.-F. Fortin, W.-J. Ma and W. Skiba, Six-point conformal blocks in the snowflake channel, JHEP 11 (2020) 147 [arXiv:2004.02824] [INSPIRE].
I. Buric et al., From Gaudin Integrable Models to d-dimensional Multipoint Conformal Blocks, Phys. Rev. Lett. 126 (2021) 021602 [arXiv:2009.11882] [INSPIRE].
D. Poland and V. Prilepina, Recursion relations for 5-point conformal blocks, JHEP 10 (2021) 160 [arXiv:2103.12092] [INSPIRE].
C. Bercini, V. Gonçalves and P. Vieira, Light-Cone Bootstrap of Higher Point Functions and Wilson Loop Duality, Phys. Rev. Lett. 126 (2021) 121603 [arXiv:2008.10407] [INSPIRE].
A. Antunes, M.S. Costa, V. Gonçalves and J.V. Boas, Lightcone bootstrap at higher points, JHEP 03 (2022) 139 [arXiv:2111.05453] [INSPIRE].
A. Kaviraj, J.A. Mann, L. Quintavalle and V. Schomerus, Multipoint lightcone bootstrap from differential equations, JHEP 08 (2023) 011 [arXiv:2212.10578] [INSPIRE].
D. Poland, V. Prilepina and P. Tadić, The five-point bootstrap, JHEP 10 (2023) 153 [arXiv:2305.08914] [INSPIRE].
S. Giombi, R. Roiban and A.A. Tseytlin, Half-BPS Wilson loop and AdS2/CFT1, Nucl. Phys. B 922 (2017) 499 [arXiv:1706.00756] [INSPIRE].
N. Drukker, Integrable Wilson loops, JHEP 10 (2013) 135 [arXiv:1203.1617] [INSPIRE].
D. Correa, J. Maldacena and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation, JHEP 08 (2012) 134 [arXiv:1203.1913] [INSPIRE].
N. Kiryu and S. Komatsu, Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization, JHEP 02 (2019) 090 [arXiv:1812.04593] [INSPIRE].
D. Grabner, N. Gromov and J. Julius, Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve, JHEP 07 (2020) 042 [arXiv:2001.11039] [INSPIRE].
A. Cavaglià, N. Gromov, J. Julius and M. Preti, Integrability and conformal bootstrap: One dimensional defect conformal field theory, Phys. Rev. D 105 (2022) L021902 [arXiv:2107.08510] [INSPIRE].
A. Cavaglià, N. Gromov, J. Julius and M. Preti, Bootstrability in defect CFT: integrated correlators and sharper bounds, JHEP 05 (2022) 164 [arXiv:2203.09556] [INSPIRE].
D. Correa, J. Henn, J. Maldacena and A. Sever, An exact formula for the radiation of a moving quark in N = 4 super Yang Mills, JHEP 06 (2012) 048 [arXiv:1202.4455] [INSPIRE].
S. Giombi and S. Komatsu, Exact Correlators on the Wilson Loop in \( \mathcal{N} \) = 4 SYM: Localization, Defect CFT, and Integrability, JHEP 05 (2018) 109 [Erratum ibid. 11 (2018) 123] [arXiv:1802.05201] [INSPIRE].
S. Giombi and S. Komatsu, More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve, J. Phys. A 52 (2019) 125401 [arXiv:1811.02369] [INSPIRE].
P. Liendo, C. Meneghelli and V. Mitev, Bootstrapping the half-BPS line defect, JHEP 10 (2018) 077 [arXiv:1806.01862] [INSPIRE].
P. Ferrero and C. Meneghelli, Bootstrapping the half-BPS line defect CFT in N = 4 supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. D 104 (2021) L081703 [arXiv:2103.10440] [INSPIRE].
J. Barrat, P. Liendo, G. Peveri and J. Plefka, Multipoint correlators on the supersymmetric Wilson line defect CFT, JHEP 08 (2022) 067 [arXiv:2112.10780] [INSPIRE].
J. Barrat, P. Liendo and G. Peveri, Multipoint correlators on the supersymmetric Wilson line defect CFT. Part II. Unprotected operators, JHEP 08 (2023) 198 [arXiv:2210.14916] [INSPIRE].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999) 125006 [hep-th/9904191] [INSPIRE].
G. Bliard, Notes on n-point Witten diagrams in AdS2, J. Phys. A 55 (2022) 325401 [arXiv:2204.01659] [INSPIRE].
S. Giombi, S. Komatsu and B. Offertaler, Chaos and the reparametrization mode on the AdS2 string, JHEP 09 (2023) 023 [arXiv:2212.14842] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
Y.-H. Qi, S.-J. Sin and J. Yoon, Quantum Correction to Chaos in Schwarzian Theory, JHEP 11 (2019) 035 [arXiv:1906.00996] [INSPIRE].
A.M. Polyakov and V.S. Rychkov, Loop dynamics and AdS/CFT correspondence, Nucl. Phys. B 594 (2001) 272 [hep-th/0005173] [INSPIRE].
V.S. Rychkov, Wilson loops, D-branes, and reparametrization path integrals, JHEP 12 (2002) 068 [hep-th/0204250] [INSPIRE].
Y. Makeenko and P. Olesen, Quantum corrections from a path integral over reparametrizations, Phys. Rev. D 82 (2010) 045025 [arXiv:1002.0055] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
A.M. Polyakov, Gauge fields and strings, Taylor & Francis (1987), p. 183–184 [https://doi.org/10.1201/9780203755082].
A.G. Cohen, G.W. Moore, P.C. Nelson and J. Polchinski, An Off-Shell Propagator for String Theory, Nucl. Phys. B 267 (1986) 143 [INSPIRE].
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
A.M. Polyakov and V.S. Rychkov, Gauge field strings duality and the loop equation, Nucl. Phys. B 581 (2000) 116 [hep-th/0002106] [INSPIRE].
A.I. Larkin and Y.N. Ovchinnikov, Quasiclassical Method in the Theory of Superconductivity, JETP 28 (1969) 1200.
A. Kitaev, A simple model of quantum holography (part 1), talk at KITP, April 7, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev/.
A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, May 27, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/.
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
S.H. Shenker and D. Stanford, Multiple Shocks, JHEP 12 (2014) 046 [arXiv:1312.3296] [INSPIRE].
B.-W. Xiao, On the exact solution of the accelerating string in AdS5 space, Phys. Lett. B 665 (2008) 173 [arXiv:0804.1343] [INSPIRE].
K. Jensen and A. Karch, Holographic Dual of an Einstein-Podolsky-Rosen Pair has a Wormhole, Phys. Rev. Lett. 111 (2013) 211602 [arXiv:1307.1132] [INSPIRE].
J. Sonner, Holographic Schwinger Effect and the Geometry of Entanglement, Phys. Rev. Lett. 111 (2013) 211603 [arXiv:1307.6850] [INSPIRE].
J. de Boer, E. Llabrés, J.F. Pedraza and D. Vegh, Chaotic strings in AdS/CFT, Phys. Rev. Lett. 120 (2018) 201604 [arXiv:1709.01052] [INSPIRE].
H.T. Lam, T.G. Mertens, G.J. Turiaci and H. Verlinde, Shockwave S-matrix from Schwarzian Quantum Mechanics, JHEP 11 (2018) 182 [arXiv:1804.09834] [INSPIRE].
K. Murata, Fast scrambling in holographic Einstein-Podolsky-Rosen pair, JHEP 11 (2017) 049 [arXiv:1708.09493] [INSPIRE].
T. Okuda and J. Penedones, String scattering in flat space and a scaling limit of Yang-Mills correlators, Phys. Rev. D 83 (2011) 086001 [arXiv:1002.2641] [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
M.F. Paulos et al., The S-matrix bootstrap. Part I: QFT in AdS, JHEP 11 (2017) 133 [arXiv:1607.06109] [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS2 holography and \( T\overline{T} \), JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].
E. Hijano, Flat space physics from AdS/CFT, JHEP 07 (2019) 132 [arXiv:1905.02729] [INSPIRE].
S. Komatsu, M.F. Paulos, B.C. Van Rees and X. Zhao, Landau diagrams in AdS and S-matrices from conformal correlators, JHEP 11 (2020) 046 [arXiv:2007.13745] [INSPIRE].
Y.-Z. Li, Notes on flat-space limit of AdS/CFT, JHEP 09 (2021) 027 [arXiv:2106.04606] [INSPIRE].
L. Córdova, Y. He and M.F. Paulos, From conformal correlators to analytic S-matrices: CFT1/QFT2, JHEP 08 (2022) 186 [arXiv:2203.10840] [INSPIRE].
B.C. van Rees and X. Zhao, Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms, Phys. Rev. Lett. 130 (2023) 191601 [arXiv:2210.15683] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. D’Hoker et al., Graviton exchange and complete four point functions in the AdS / CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th/9903196] [INSPIRE].
N. Callebaut, S.S. Gubser, A. Samberg and C. Toldo, Segmented strings in AdS3, JHEP 11 (2015) 110 [arXiv:1508.07311] [INSPIRE].
D. Vegh, The broken string in anti-de Sitter space, JHEP 02 (2018) 045 [arXiv:1508.06637] [INSPIRE].
D. Vegh, Colliding waves on a string in AdS3, arXiv:1509.05033 [INSPIRE].
A. Milekhin, Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models, JHEP 12 (2021) 114 [arXiv:2102.06647] [INSPIRE].
A. Milekhin, Coupled Sachdev-Ye-Kitaev models without Schwartzian dominance, arXiv:2102.06651 [INSPIRE].
Acknowledgments
The work of SG, BO and JS is supported in part by the US NSF under Grant No. PHY-2209997. SG is grateful to the Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA* (Project ID 39083149) for its hospitality and its partial support during completion of this work.
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Giombi, S., Komatsu, S., Offertaler, B. et al. Boundary reparametrizations and six-point functions on the AdS2 string. J. High Energ. Phys. 2024, 196 (2024). https://doi.org/10.1007/JHEP08(2024)196
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DOI: https://doi.org/10.1007/JHEP08(2024)196