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Holographic relations for OPE blocks in excited states. (English) Zbl 1414.81200

Summary: We study the holographic duality between boundary OPE blocks and geodesic integrated bulk fields in quotients of \(\mathrm{AdS}_3\) dual to excited CFT states. The quotient geometries exhibit non-minimal geodesics between pairs of spacelike separated boundary points which modify the OPE block duality. We decompose OPE blocks into quotient invariant operators and propose a duality with bulk fields integrated over individual geodesics, minimal or non-minimal. We provide evidence for this relationship by studying the monodromy of asymptotic maps that implement the quotients.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83E05 Geometrodynamics and the holographic principle
53Z05 Applications of differential geometry to physics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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[1] J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE]. · Zbl 0969.81047 · doi:10.1023/A:1026654312961
[2] S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP08 (2006) 045 [hep-th/0605073] [INSPIRE]. · Zbl 1228.83110 · doi:10.1088/1126-6708/2006/08/045
[3] M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav.42 (2010) 2323 [arXiv:1005.3035] [INSPIRE]. · Zbl 1200.83052 · doi:10.1007/s10714-010-1034-0
[4] T. Faulkner, F.M. Haehl, E. Hijano, O. Parrikar, C. Rabideau and M. Van Raamsdonk, Nonlinear Gravity from Entanglement in Conformal Field Theories, JHEP08 (2017) 057 [arXiv:1705.03026] [INSPIRE]. · Zbl 1381.83099 · doi:10.1007/JHEP08(2017)057
[5] A. Almheiri, X. Dong and D. Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT, JHEP04 (2015) 163 [arXiv:1411.7041] [INSPIRE]. · Zbl 1388.81095 · doi:10.1007/JHEP04(2015)163
[6] E. Mintun, J. Polchinski and V. Rosenhaus, Bulk-Boundary Duality, Gauge Invariance and Quantum Error Corrections, Phys. Rev. Lett.115 (2015) 151601 [arXiv:1501.06577] [INSPIRE]. · doi:10.1103/PhysRevLett.115.151601
[7] F. Pastawski, B. Yoshida, D. Harlow and J. Preskill, Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence, JHEP06 (2015) 149 [arXiv:1503.06237] [INSPIRE]. · Zbl 1388.81094 · doi:10.1007/JHEP06(2015)149
[8] L. Susskind, Computational Complexity and Black Hole Horizons, Fortsch. Phys.64 (2016) 44 [arXiv:1403.5695] [INSPIRE]. · Zbl 1429.81020 · doi:10.1002/prop.201500093
[9] T. Takayanagi and K. Umemoto, Entanglement of purification through holographic duality, Nature Phys.14 (2018) 573 [arXiv:1708.09393] [INSPIRE]. · doi:10.1038/s41567-018-0075-2
[10] B. Czech, L. Lamprou, S. McCandlish and J. Sully, Integral Geometry and Holography, JHEP10 (2015) 175 [arXiv:1505.05515] [INSPIRE]. · Zbl 1388.83217 · doi:10.1007/JHEP10(2015)175
[11] B. Czech, L. Lamprou, S. McCandlish, B. Mosk and J. Sully, A Stereoscopic Look into the Bulk, JHEP07 (2016) 129 [arXiv:1604.03110] [INSPIRE]. · Zbl 1390.83101 · doi:10.1007/JHEP07(2016)129
[12] J. de Boer, F.M. Haehl, M.P. Heller and R.C. Myers, Entanglement, holography and causal diamonds, JHEP08 (2016) 162 [arXiv:1606.03307] [INSPIRE]. · Zbl 1390.83135 · doi:10.1007/JHEP08(2016)162
[13] E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks, JHEP01 (2016) 146 [arXiv:1508.00501] [INSPIRE]. · Zbl 1388.81047 · doi:10.1007/JHEP01(2016)146
[14] E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Semiclassical Virasoro blocks from AdS3gravity, JHEP12 (2015) 077 [arXiv:1508.04987] [INSPIRE]. · Zbl 1388.81940
[15] M. Fukuda, N. Kobayashi and T. Nishioka, Operator product expansion for conformal defects, JHEP01 (2018) 013 [arXiv:1710.11165] [INSPIRE]. · Zbl 1384.81100 · doi:10.1007/JHEP01(2018)013
[16] N. Kobayashi and T. Nishioka, Spinning conformal defects, JHEP09 (2018) 134 [arXiv:1805.05967] [INSPIRE]. · Zbl 1398.81214 · doi:10.1007/JHEP09(2018)134
[17] G. Sárosi and T. Ugajin, Modular Hamiltonians of excited states, OPE blocks and emergent bulk fields, JHEP01 (2018) 012 [arXiv:1705.01486] [INSPIRE]. · Zbl 1384.81120 · doi:10.1007/JHEP01(2018)012
[18] B. Czech, L. Lamprou, S. McCandlish and J. Sully, Tensor Networks from Kinematic Space, JHEP07 (2016) 100 [arXiv:1512.01548] [INSPIRE]. · Zbl 1390.83102 · doi:10.1007/JHEP07(2016)100
[19] C.T. Asplund, N. Callebaut and C. Zukowski, Equivalence of Emergent de Sitter Spaces from Conformal Field Theory, JHEP09 (2016) 154 [arXiv:1604.02687] [INSPIRE]. · Zbl 1390.83079 · doi:10.1007/JHEP09(2016)154
[20] J.-d. Zhang and B. Chen, Kinematic Space and Wormholes, JHEP01 (2017) 092 [arXiv:1610.07134] [INSPIRE]. · Zbl 1373.83073 · doi:10.1007/JHEP01(2017)092
[21] A. Karch, J. Sully, C.F. Uhlemann and D.G.E. Walker, Boundary Kinematic Space, JHEP08 (2017) 039 [arXiv:1703.02990] [INSPIRE]. · Zbl 1381.81116 · doi:10.1007/JHEP08(2017)039
[22] J.C. Cresswell and A.W. Peet, Kinematic space for conical defects, JHEP11 (2017) 155 [arXiv:1708.09838] [INSPIRE]. · Zbl 1383.81198 · doi:10.1007/JHEP11(2017)155
[23] R. Abt et al., Topological Complexity in AdS3/CFT2, Fortsch. Phys.66 (2018) 1800034 [arXiv:1710.01327] [INSPIRE].
[24] R. Abt, J. Erdmenger, M. Gerbershagen, C.M. Melby-Thompson and C. Northe, Holographic Subregion Complexity from Kinematic Space, JHEP01 (2019) 012 [arXiv:1805.10298] [INSPIRE]. · Zbl 1409.83083 · doi:10.1007/JHEP01(2019)012
[25] V. Balasubramanian and S.F. Ross, Holographic particle detection, Phys. Rev.D 61 (2000) 044007 [hep-th/9906226] [INSPIRE].
[26] 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].
[27] O. Lunin, J.M. Maldacena and L. Maoz, Gravity solutions for the D1-D5 system with angular momentum, hep-th/0212210 [INSPIRE].
[28] V. Balasubramanian, B.D. Chowdhury, B. Czech and J. de Boer, Entwinement and the emergence of spacetime, JHEP01 (2015) 048 [arXiv:1406.5859] [INSPIRE]. · Zbl 1388.83633 · doi:10.1007/JHEP01(2015)048
[29] V. Balasubramanian, A. Bernamonti, B. Craps, T. De Jonckheere and F. Galli, Entwinement in discretely gauged theories, JHEP12 (2016) 094 [arXiv:1609.03991] [INSPIRE]. · Zbl 1390.83084 · doi:10.1007/JHEP12(2016)094
[30] M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev.D 48 (1993) 1506 [Erratum ibid.D 88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
[31] S. Carlip and C. Teitelboim, Aspects of black hole quantum mechanics and thermodynamics in (2+1)-dimensions, Phys. Rev.D 51 (1995) 622 [gr-qc/9405070] [INSPIRE].
[32] C.-B. Chen, W.-C. Gan, F.-W. Shu and B. Xiong, Quantum information metric of conical defect, Phys. Rev.D 98 (2018) 046008 [arXiv:1804.08358] [INSPIRE].
[33] L.F. Alday, J. de Boer and I. Messamah, The Gravitational description of coarse grained microstates, JHEP12 (2006) 063 [hep-th/0607222] [INSPIRE]. · Zbl 1226.83054 · doi:10.1088/1126-6708/2006/12/063
[34] M. Bañados, Three-dimensional quantum geometry and black holes, AIP Conf. Proc.484 (1999) 147 [hep-th/9901148] [INSPIRE]. · Zbl 1162.83342 · doi:10.1063/1.59661
[35] M.M. Roberts, Time evolution of entanglement entropy from a pulse, JHEP12 (2012) 027 [arXiv:1204.1982] [INSPIRE]. · doi:10.1007/JHEP12(2012)027
[36] J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys.104 (1986) 207 [INSPIRE]. · Zbl 0584.53039 · doi:10.1007/BF01211590
[37] C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches, JHEP02 (2015) 171 [arXiv:1410.1392] [INSPIRE]. · Zbl 1388.83084
[38] N. Anand, H. Chen, A.L. Fitzpatrick, J. Kaplan and D. Li, An Exact Operator That Knows Its Location, JHEP02 (2018) 012 [arXiv:1708.04246] [INSPIRE]. · Zbl 1387.81297 · doi:10.1007/JHEP02(2018)012
[39] A. de la Fuente and R. Sundrum, Holography of the BTZ Black Hole, Inside and Out, JHEP09 (2014) 073 [arXiv:1307.7738] [INSPIRE]. · Zbl 1333.83098 · doi:10.1007/JHEP09(2014)073
[40] K. Goto and T. Takayanagi, CFT descriptions of bulk local states in the AdS black holes, JHEP10 (2017) 153 [arXiv:1704.00053] [INSPIRE]. · Zbl 1383.83057 · doi:10.1007/JHEP10(2017)153
[41] H. Maxfield, Entanglement entropy in three dimensional gravity, JHEP04 (2015) 031 [arXiv:1412.0687] [INSPIRE]. · Zbl 1388.83555 · doi:10.1007/JHEP04(2015)031
[42] V. Balasubramanian, A. Naqvi and J. Simon, A Multiboundary AdS orbifold and DLCQ holography: A Universal holographic description of extremal black hole horizons, JHEP08 (2004) 023 [hep-th/0311237] [INSPIRE]. · doi:10.1088/1126-6708/2004/08/023
[43] I.Y. Aref’eva and M.A. Khramtsov, AdS/CFT prescription for angle-deficit space and winding geodesics, JHEP04 (2016) 121 [arXiv:1601.02008] [INSPIRE].
[44] D. Pappadopulo, S. Rychkov, J. Espin and R. Rattazzi, OPE Convergence in Conformal Field Theory, Phys. Rev.D 86 (2012) 105043 [arXiv:1208.6449] [INSPIRE].
[45] S. Rychkov and P. Yvernay, Remarks on the Convergence Properties of the Conformal Block Expansion, Phys. Lett.B 753 (2016) 682 [arXiv:1510.08486] [INSPIRE]. · Zbl 1367.81127
[46] E. Keski-Vakkuri, Bulk and boundary dynamics in BTZ black holes, Phys. Rev.D 59 (1999) 104001 [hep-th/9808037] [INSPIRE].
[47] V. Balasubramanian et al., Thermalization of the spectral function in strongly coupled two dimensional conformal field theories, JHEP04 (2013) 069 [arXiv:1212.6066] [INSPIRE]. · Zbl 1342.81476 · doi:10.1007/JHEP04(2013)069
[48] G.T. Horowitz and D. Marolf, A New approach to string cosmology, JHEP07 (1998) 014 [hep-th/9805207] [INSPIRE]. · Zbl 0951.83036 · doi:10.1088/1126-6708/1998/07/014
[49] P. Banerjee, S. Datta and R. Sinha, Higher-point conformal blocks and entanglement entropy in heavy states, JHEP05 (2016) 127 [arXiv:1601.06794] [INSPIRE]. · Zbl 1388.83171 · doi:10.1007/JHEP05(2016)127
[50] T. Anous, T. Hartman, A. Rovai and J. Sonner, Black Hole Collapse in the 1/c Expansion, JHEP07 (2016) 123 [arXiv:1603.04856] [INSPIRE]. · Zbl 1390.83170 · doi:10.1007/JHEP07(2016)123
[51] T. Anous, T. Hartman, A. Rovai and J. Sonner, From Conformal Blocks to Path Integrals in the Vaidya Geometry, JHEP09 (2017) 009 [arXiv:1706.02668] [INSPIRE]. · Zbl 1382.81165 · doi:10.1007/JHEP09(2017)009
[52] B. Carneiro da Cunha and M. Guica, Exploring the BTZ bulk with boundary conformal blocks, arXiv:1604.07383 [INSPIRE].
[53] A. Maloney, H. Maxfield and G.S. Ng, A conformal block Farey tail, JHEP06 (2017) 117 [arXiv:1609.02165] [INSPIRE]. · Zbl 1380.81345 · doi:10.1007/JHEP06(2017)117
[54] V. Balasubramanian, B. Craps, T. De Jonckheere and G. Sárosi, Entanglement versus entwinement in symmetric product orbifolds, JHEP01 (2019) 190 [arXiv:1806.02871] [INSPIRE]. · Zbl 1409.81012 · doi:10.1007/JHEP01(2019)190
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