Abstract
We examine the Regge limit of holographic 4-point correlation functions in AdS3 × S3 involving two heavy and two light operators. In this kinematic regime such correlators can be reconstructed from the bulk phase shift accumulated by the light probe as it traverses the geometry dual to the heavy operator. We work perturbatively — but to arbitrary orders — in the ratio of the heavy operator’s conformal dimension to the dual CFT2’s central charge, thus going beyond the low order results of [1] and [2]. In doing so, we derive all-order relations between the bulk phase shift and the Regge limit OPE data of a class of heavy-light multi-trace operators exchanged in the cross-channel. Furthermore, we analyse two examples for which the relevant 4-point correlators are known explicitly to all orders: firstly the case of heavy operators dual to AdS3 conical defect geometries and secondly the case of non-trivial smooth geometries representing microstates of the two-charge D1-D5 black hole.
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References
M. Kulaxizi, G. S. Ng and A. Parnachev, Black Holes, Heavy States, Phase Shift and Anomalous Dimensions, SciPost Phys. 6 (2019) 065 [arXiv:1812.03120] [INSPIRE].
S. Giusto, M. R. R. Hughes and R. Russo, The Regge limit of AdS3 holographic correlators, JHEP 11 (2020) 018 [arXiv:2007.12118] [INSPIRE].
M. Levy and J. Sucher, Eikonal approximation in quantum field theory, Phys. Rev. 186 (1969) 1656 [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Superstring Collisions at Planckian Energies, Phys. Lett. B 197 (1987) 81 [INSPIRE].
G. ’t Hooft, Graviton Dominance in Ultrahigh-Energy Scattering, Phys. Lett. B 198 (1987) 61 [INSPIRE].
J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
L. Cornalba, M. S. Costa, J. Penedones and R. Schiappa, Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions, JHEP 08 (2007) 019 [hep-th/0611122] [INSPIRE].
L. Cornalba, M. S. Costa, J. Penedones and R. Schiappa, Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions, Nucl. Phys. B 767 (2007) 327 [hep-th/0611123] [INSPIRE].
L. Cornalba, M. S. Costa and J. Penedones, Eikonal approximation in AdS/CFT: Resumming the gravitational loop expansion, JHEP 09 (2007) 037 [arXiv:0707.0120] [INSPIRE].
L. Cornalba, Eikonal methods in AdS/CFT: Regge theory and multi-reggeon exchange, arXiv:0710.5480 [INSPIRE].
A. L. Fitzpatrick, J. Kaplan and M. T. Walters, Universality of Long-Distance AdS Physics from the CFT Bootstrap, JHEP 08 (2014) 145 [arXiv:1403.6829] [INSPIRE].
A. L. Fitzpatrick, J. Kaplan and M. T. Walters, Virasoro Conformal Blocks and Thermality from Classical Background Fields, JHEP 11 (2015) 200 [arXiv:1501.05315] [INSPIRE].
L. Cornalba, M. S. Costa and J. Penedones, Deep Inelastic Scattering in Conformal QCD, JHEP 03 (2010) 133 [arXiv:0911.0043] [INSPIRE].
M. S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].
M. Kulaxizi, A. Parnachev and A. Zhiboedov, Bulk Phase Shift, CFT Regge Limit and Einstein Gravity, JHEP 06 (2018) 121 [arXiv:1705.02934] [INSPIRE].
D. Li, D. Meltzer and D. Poland, Conformal Bootstrap in the Regge Limit, JHEP 12 (2017) 013 [arXiv:1705.03453] [INSPIRE].
R. Karlsson, M. Kulaxizi, A. Parnachev and P. Tadić, Leading Multi-Stress Tensors and Conformal Bootstrap, JHEP 01 (2020) 076 [arXiv:1909.05775] [INSPIRE].
R. Karlsson, M. Kulaxizi, A. Parnachev and P. Tadić, Black Holes and Conformal Regge Bootstrap, JHEP 10 (2019) 046 [arXiv:1904.00060] [INSPIRE].
Y.-Z. Li and H.-Y. Zhang, More on heavy-light bootstrap up to double-stress-tensor, JHEP 10 (2020) 055 [arXiv:2004.04758] [INSPIRE].
L. Cornalba, M. S. Costa and J. Penedones, Eikonal Methods in AdS/CFT: BFKL Pomeron at Weak Coupling, JHEP 06 (2008) 048 [arXiv:0801.3002] [INSPIRE].
R. C. Brower, M. J. Strassler and C.-I. Tan, On The Pomeron at Large ’t Hooft Coupling, JHEP 03 (2009) 092 [arXiv:0710.4378] [INSPIRE].
D. Meltzer, AdS/CFT Unitarity at Higher Loops: High-Energy String Scattering, JHEP 05 (2020) 133 [arXiv:1912.05580] [INSPIRE].
A. Antunes, M. S. Costa, T. Hansen, A. Salgarkar and S. Sarkar, The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop, JHEP 04 (2021) 088 [arXiv:2012.01515] [INSPIRE].
A. Strominger, Black hole entropy from near horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [INSPIRE].
S. D. Mathur, The fuzzball proposal for black holes: An elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].
S. D. Mathur, Fuzzballs and the information paradox: A summary and conjectures, arXiv:0810.4525 [INSPIRE].
A. Galliani, S. Giusto, E. Moscato and R. Russo, Correlators at large c without information loss, JHEP 09 (2016) 065 [arXiv:1606.01119] [INSPIRE].
A. Galliani, S. Giusto and R. Russo, Holographic 4-point correlators with heavy states, JHEP 10 (2017) 040 [arXiv:1705.09250] [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. Bombini and A. Galliani, AdS3 four-point functions from \( \frac{1}{8} \)-BPS states, JHEP 06 (2019) 044 [arXiv:1904.02656] [INSPIRE].
L. Rastelli, K. Roumpedakis and X. Zhou, AdS3 × S3 Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry, JHEP 10 (2019) 140 [arXiv:1905.11983] [INSPIRE].
N. Čeplak, S. Giusto, M. R. R. Hughes and R. Russo, to appear.
D. Zagier, Polylogarithms, dedekind zeta functions, and the algebraic k-theory of fields, in Arithmetic algebraic geometry, Springer (1991), pp. 391–430.
V. Balasubramanian, J. de Boer, E. Keski-Vakkuri and S. F. Ross, Supersymmetric conical defects: Towards a string theoretic description of black hole formation, Phys. Rev. D 64 (2001) 064011 [hep-th/0011217] [INSPIRE].
J. M. Maldacena and L. Maoz, Desingularization by rotation, JHEP 12 (2002) 055 [hep-th/0012025] [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].
Z. Bern et al., Scattering Amplitudes and Conservative Binary Dynamics at \( \mathcal{O}\left({G}^4\right) \), Phys. Rev. Lett. 126 (2021) 171601 [arXiv:2101.07254] [INSPIRE].
A. Parnachev and K. Sen, Notes on AdS-Schwarzschild eikonal phase, JHEP 03 (2021) 289 [arXiv:2011.06920] [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].
S. B. Giddings, The boundary S matrix and the AdS to CFT dictionary, Phys. Rev. Lett. 83 (1999) 2707 [hep-th/9903048] [INSPIRE].
J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Unmixing Supergravity, JHEP 02 (2018) 133 [arXiv:1706.08456] [INSPIRE].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP 06 (2007) 056 [arXiv:0704.0690] [INSPIRE].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2+1) black hole, Phys. Rev. D 48 (1993) 1506 [Erratum ibid. 88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
I. Bena et al., Asymptotically-flat supergravity solutions deep inside the black-hole regime, JHEP 02 (2018) 014 [arXiv:1711.10474] [INSPIRE].
S. Giusto, R. Russo and C. Wen, Holographic correlators in AdS3, JHEP 03 (2019) 096 [arXiv:1812.06479] [INSPIRE].
S. Giusto, R. Russo, A. Tyukov and C. Wen, Holographic correlators in AdS3 without Witten diagrams, JHEP 09 (2019) 030 [arXiv:1905.12314] [INSPIRE].
S. Giusto, R. Russo, A. Tyukov and C. Wen, The CFT6 origin of all tree-level 4-point correlators in AdS3 × S3, Eur. Phys. J. C 80 (2020) 736 [arXiv:2005.08560] [INSPIRE].
L. Lewin, Polylogarithms and associated functions, North-Holland, New York, NY U.S.A. (1981).
D. Ramakrishnan, Analogs of the bloch-wigner function for higher polylogarithms, Contemp. Math. 55 (1986) 371.
D. Zagier, The bloch-wigner-ramakrishnan polylogarithm function, Math. Ann. 286 (1990) 613.
D. Zagier, The dilogarithm function, in Frontiers in Number Theory, Physics and Geometry II, Springer-Verlag, Berlin-Heidelberg-New York (2006), pp. 3–65.
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Čeplak, N., Hughes, M.R.R. The Regge limit of AdS3 holographic correlators with heavy states: towards the black hole regime. J. High Energ. Phys. 2021, 21 (2021). https://doi.org/10.1007/JHEP07(2021)021
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DOI: https://doi.org/10.1007/JHEP07(2021)021