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The Regge limit of \( \mathrm{AdS}_3\) holographic correlators with heavy states: towards the black hole regime. (English) Zbl 1468.83037

Summary: We examine the Regge limit of holographic 4-point correlation functions in \( \mathrm{AdS}_3 \times S^3\) 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 \( \mathrm{CFT}_2\)’s central charge, thus going beyond the low order results of [S. Giusto et al., J. High Energy Phys. 2020, No. 11, Paper No. 18, 37 p. (2020; Zbl 1456.83079)]. 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 \( \mathrm{AdS}_3\) conical defect geometries and secondly the case of non-trivial smooth geometries representing microstates of the two-charge D1-D5 black hole.

MSC:

83E05 Geometrodynamics and the holographic principle
83C27 Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory
83C57 Black holes
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R15 Operator algebra methods applied to problems in quantum theory

Citations:

Zbl 1456.83079

References:

[1] Kulaxizi, M.; Ng, GS; Parnachev, A., Black Holes, Heavy States, Phase Shift and Anomalous Dimensions, SciPost Phys., 6, 065 (2019) · doi:10.21468/SciPostPhys.6.6.065
[2] Giusto, S.; Hughes, MRR; Russo, R., The Regge limit of AdS_3holographic correlators, JHEP, 11, 018 (2020) · Zbl 1456.83079 · doi:10.1007/JHEP11(2020)018
[3] Levy, M.; Sucher, J., Eikonal approximation in quantum field theory, Phys. Rev., 186, 1656 (1969) · doi:10.1103/PhysRev.186.1656
[4] Amati, D.; Ciafaloni, M.; Veneziano, G., Superstring Collisions at Planckian Energies, Phys. Lett. B, 197, 81 (1987) · doi:10.1016/0370-2693(87)90346-7
[5] G. ’t Hooft, Graviton Dominance in Ultrahigh-Energy Scattering, Phys. Lett. B198 (1987) 61 [INSPIRE].
[6] Maldacena, JM, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys., 2, 231 (1998) · Zbl 0914.53047 · doi:10.4310/ATMP.1998.v2.n2.a1
[7] Cornalba, L.; Costa, MS; Penedones, J.; Schiappa, R., Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions, JHEP, 08, 019 (2007) · Zbl 1326.81147 · doi:10.1088/1126-6708/2007/08/019
[8] Cornalba, L.; Costa, MS; Penedones, J.; Schiappa, R., Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions, Nucl. Phys. B, 767, 327 (2007) · Zbl 1326.81147 · doi:10.1016/j.nuclphysb.2007.01.007
[9] Cornalba, L.; Costa, MS; Penedones, J., Eikonal approximation in AdS/CFT: Resumming the gravitational loop expansion, JHEP, 09, 037 (2007) · doi:10.1088/1126-6708/2007/09/037
[10] L. Cornalba, Eikonal methods in AdS/CFT: Regge theory and multi-reggeon exchange, arXiv:0710.5480 [INSPIRE].
[11] Fitzpatrick, AL; Kaplan, J.; Walters, MT, Universality of Long-Distance AdS Physics from the CFT Bootstrap, JHEP, 08, 145 (2014) · doi:10.1007/JHEP08(2014)145
[12] Fitzpatrick, AL; Kaplan, J.; Walters, MT, Virasoro Conformal Blocks and Thermality from Classical Background Fields, JHEP, 11, 200 (2015) · Zbl 1388.83239 · doi:10.1007/JHEP11(2015)200
[13] Cornalba, L.; Costa, MS; Penedones, J., Deep Inelastic Scattering in Conformal QCD, JHEP, 03, 133 (2010) · Zbl 1271.81170 · doi:10.1007/JHEP03(2010)133
[14] Costa, MS; Goncalves, V.; Penedones, J., Conformal Regge theory, JHEP, 12, 091 (2012) · Zbl 1397.81297 · doi:10.1007/JHEP12(2012)091
[15] Kulaxizi, M.; Parnachev, A.; Zhiboedov, A., Bulk Phase Shift, CFT Regge Limit and Einstein Gravity, JHEP, 06, 121 (2018) · Zbl 1395.83012 · doi:10.1007/JHEP06(2018)121
[16] Li, D.; Meltzer, D.; Poland, D., Conformal Bootstrap in the Regge Limit, JHEP, 12, 013 (2017) · Zbl 1383.81242 · doi:10.1007/JHEP12(2017)013
[17] Karlsson, R.; Kulaxizi, M.; Parnachev, A.; Tadić, P., Leading Multi-Stress Tensors and Conformal Bootstrap, JHEP, 01, 076 (2020) · Zbl 1434.81104 · doi:10.1007/JHEP01(2020)076
[18] Karlsson, R.; Kulaxizi, M.; Parnachev, A.; Tadić, P., Black Holes and Conformal Regge Bootstrap, JHEP, 10, 046 (2019) · Zbl 1427.83040 · doi:10.1007/JHEP10(2019)046
[19] Li, Y-Z; Zhang, H-Y, More on heavy-light bootstrap up to double-stress-tensor, JHEP, 10, 055 (2020)
[20] Cornalba, L.; Costa, MS; Penedones, J., Eikonal Methods in AdS/CFT: BFKL Pomeron at Weak Coupling, JHEP, 06, 048 (2008) · doi:10.1088/1126-6708/2008/06/048
[21] Brower, RC; Strassler, MJ; Tan, C-I, On The Pomeron at Large ’t Hooft Coupling, JHEP, 03, 092 (2009) · doi:10.1088/1126-6708/2009/03/092
[22] Meltzer, D., AdS/CFT Unitarity at Higher Loops: High-Energy String Scattering, JHEP, 05, 133 (2020) · Zbl 1437.83143 · doi:10.1007/JHEP05(2020)133
[23] Antunes, A.; Costa, MS; Hansen, T.; Salgarkar, A.; Sarkar, S., The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop, JHEP, 04, 088 (2021) · Zbl 1462.83062 · doi:10.1007/JHEP04(2021)088
[24] Strominger, A., Black hole entropy from near horizon microstates, JHEP, 02, 009 (1998) · Zbl 0955.83010 · doi:10.1088/1126-6708/1998/02/009
[25] Mathur, SD, The fuzzball proposal for black holes: An elementary review, Fortsch. Phys., 53, 793 (2005) · Zbl 1116.83300 · doi:10.1002/prop.200410203
[26] S. D. Mathur, Fuzzballs and the information paradox: A summary and conjectures, arXiv:0810.4525 [INSPIRE].
[27] Galliani, A.; Giusto, S.; Moscato, E.; Russo, R., Correlators at large c without information loss, JHEP, 09, 065 (2016) · Zbl 1390.83107 · doi:10.1007/JHEP09(2016)065
[28] Galliani, A.; Giusto, S.; Russo, R., Holographic 4-point correlators with heavy states, JHEP, 10, 040 (2017) · Zbl 1383.81212 · doi:10.1007/JHEP10(2017)040
[29] Bombini, A.; Galliani, A.; Giusto, S.; Moscato, E.; Russo, R., Unitary 4-point correlators from classical geometries, Eur. Phys. J. C, 78, 8 (2018) · doi:10.1140/epjc/s10052-017-5492-3
[30] Bombini, A.; Galliani, A., AdS_3four-point functions from \(\frac{1}{8} \)-BPS states, JHEP, 06, 044 (2019) · Zbl 1416.83041 · doi:10.1007/JHEP06(2019)044
[31] Rastelli, L.; Roumpedakis, K.; Zhou, X., AdS_3×S^3Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry, JHEP, 10, 140 (2019) · Zbl 1427.81147 · doi:10.1007/JHEP10(2019)140
[32] N. Čeplak, S. Giusto, M. R. R. Hughes and R. Russo, to appear.
[33] D. Zagier, Polylogarithms, dedekind zeta functions, and the algebraic k-theory of fields, in Arithmetic algebraic geometry, Springer (1991), pp. 391-430. · Zbl 0728.11062
[34] Balasubramanian, V.; de Boer, J.; Keski-Vakkuri, E.; Ross, SF, Supersymmetric conical defects: Towards a string theoretic description of black hole formation, Phys. Rev. D, 64, 064011 (2001) · doi:10.1103/PhysRevD.64.064011
[35] Maldacena, JM; Maoz, L., Desingularization by rotation, JHEP, 12, 055 (2002) · doi:10.1088/1126-6708/2002/12/055
[36] Lunin, O.; Mathur, SD, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B, 623, 342 (2002) · Zbl 1036.83503 · doi:10.1016/S0550-3213(01)00620-4
[37] Bern, Z., Scattering Amplitudes and Conservative Binary Dynamics at \(\mathcal{O}\left({G}^4\right) \), Phys. Rev. Lett., 126, 171601 (2021) · doi:10.1103/PhysRevLett.126.171601
[38] Parnachev, A.; Sen, K., Notes on AdS-Schwarzschild eikonal phase, JHEP, 03, 289 (2021) · Zbl 1461.83035 · doi:10.1007/JHEP03(2021)289
[39] Giddings, SB, Flat space scattering and bulk locality in the AdS/CFT correspondence, Phys. Rev. D, 61, 106008 (2000) · doi:10.1103/PhysRevD.61.106008
[40] Giddings, SB, The boundary S matrix and the AdS to CFT dictionary, Phys. Rev. Lett., 83, 2707 (1999) · Zbl 0958.81151 · doi:10.1103/PhysRevLett.83.2707
[41] J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].
[42] Penedones, J., Writing CFT correlation functions as AdS scattering amplitudes, JHEP, 03, 025 (2011) · Zbl 1301.81154 · doi:10.1007/JHEP03(2011)025
[43] Aprile, F.; Drummond, JM; Heslop, P.; Paul, H., Unmixing Supergravity, JHEP, 02, 133 (2018) · Zbl 1387.83093 · doi:10.1007/JHEP02(2018)133
[44] Heemskerk, I.; Penedones, J.; Polchinski, J.; Sully, J., Holography from Conformal Field Theory, JHEP, 10, 079 (2009) · doi:10.1088/1126-6708/2009/10/079
[45] Kanitscheider, I.; Skenderis, K.; Taylor, M., Fuzzballs with internal excitations, JHEP, 06, 056 (2007) · doi:10.1088/1126-6708/2007/06/056
[46] M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2+1) black hole, Phys. Rev. D48 (1993) 1506 [Erratum ibid.88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
[47] Bañados, M.; Teitelboim, C.; Zanelli, J., The black hole in three-dimensional space-time, Phys. Rev. Lett., 69, 1849 (1992) · Zbl 0968.83514 · doi:10.1103/PhysRevLett.69.1849
[48] Bena, I., Asymptotically-flat supergravity solutions deep inside the black-hole regime, JHEP, 02, 014 (2018) · Zbl 1387.83096 · doi:10.1007/JHEP02(2018)014
[49] Giusto, S.; Russo, R.; Wen, C., Holographic correlators in AdS_3, JHEP, 03, 096 (2019) · Zbl 1414.81205 · doi:10.1007/JHEP03(2019)096
[50] Giusto, S.; Russo, R.; Tyukov, A.; Wen, C., Holographic correlators in AdS_3without Witten diagrams, JHEP, 09, 030 (2019) · Zbl 1423.81158 · doi:10.1007/JHEP09(2019)030
[51] Giusto, S.; Russo, R.; Tyukov, A.; Wen, C., The CFT_6origin of all tree-level 4-point correlators in AdS_3× S^3, Eur. Phys. J. C, 80, 736 (2020) · doi:10.1140/epjc/s10052-020-8300-4
[52] L. Lewin, Polylogarithms and associated functions, North-Holland, New York, NY U.S.A. (1981). · Zbl 0465.33001
[53] Ramakrishnan, D., Analogs of the bloch-wigner function for higher polylogarithms, Contemp. Math., 55, 371 (1986) · Zbl 0655.12005 · doi:10.1090/conm/055.1/862642
[54] Zagier, D., The bloch-wigner-ramakrishnan polylogarithm function, Math. Ann., 286, 613 (1990) · Zbl 0698.33001 · doi:10.1007/BF01453591
[55] D. Zagier, The dilogarithm function, in Frontiers in Number Theory, Physics and Geometry II, Springer-Verlag, Berlin-Heidelberg-New York (2006), pp. 3-65. · Zbl 1176.11026
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