Toward random tensor networks and holographic codes in CFT. (English) Zbl 07701924
Summary: In holographic CFTs satisfying eigenstate thermalization, there is a regime where the operator product expansion can be approximated by a random tensor network. The geometry of the tensor network corresponds to a spatial slice in the holographic dual, with the tensors discretizing the radial direction. In spherically symmetric states in any dimension and more general states in 2d CFT, this leads to a holographic error-correcting code, defined in terms of OPE data, that can be systematically corrected beyond the random tensor approximation. The code is shown to be isometric for light operators outside the horizon, and non-isometric inside, as expected from general arguments about bulk reconstruction. The transition at the horizon occurs due to a subtle breakdown of the Virasoro identity block approximation in states with a complex interior.
MSC:
| 81T32 | Matrix models and tensor models for quantum field theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81P73 | Computational stability and error-correcting codes for quantum computation and communication processing |
References:
| [1] | B. Swingle, Entanglement renormalization and holography, Phys. Rev. D86 (2012) 065007 [arXiv:0905.1317] [INSPIRE]. |
| [2] | Harlow, D., The Ryu-Takayanagi formula from quantum error correction, Commun. Math. Phys., 354, 865 (2017) · Zbl 1377.81040 · doi:10.1007/s00220-017-2904-z |
| [3] | Hayden, P., Holographic duality from random tensor networks, JHEP, 11, 009 (2016) · Zbl 1390.83344 · doi:10.1007/JHEP11(2016)009 |
| [4] | Akers, C.; Rath, P., Holographic Renyi entropy from quantum error correction, JHEP, 05, 052 (2019) · Zbl 1416.83095 · doi:10.1007/JHEP05(2019)052 |
| [5] | Dong, X.; Harlow, D.; Marolf, D., Flat entanglement spectra in fixed-area states of quantum gravity, JHEP, 10, 240 (2019) · Zbl 1427.83020 · doi:10.1007/JHEP10(2019)240 |
| [6] | M. Van Raamsdonk, Building up spacetime with quantum entanglement II: it from BC-bit, arXiv:1809.01197 [INSPIRE]. · Zbl 1200.83052 |
| [7] | Bao, N.; Penington, G.; Sorce, J.; Wall, AC, Beyond toy models: distilling tensor networks in full AdS/CFT, JHEP, 11, 069 (2019) · Zbl 1429.81063 · doi:10.1007/JHEP11(2019)069 |
| [8] | N. Bao, G. Penington, J. Sorce and A.C. Wall, Holographic tensor networks in full AdS/CFT, arXiv:1902.10157 [INSPIRE]. |
| [9] | X. Dong, D. Harlow and A.C. Wall, Reconstruction of bulk operators within the entanglement wedge in gauge-gravity duality, Phys. Rev. Lett.117 (2016) 021601 [arXiv:1601.05416] [INSPIRE]. |
| [10] | M. Miyaji, T. Takayanagi and K. Watanabe, From path integrals to tensor networks for the AdS/CFT correspondence, Phys. Rev. D95 (2017) 066004 [arXiv:1609.04645] [INSPIRE]. · Zbl 1383.81189 |
| [11] | Takayanagi, T.; Umemoto, K., Entanglement of purification through holographic duality, Nature Phys., 14, 573 (2018) · doi:10.1038/s41567-018-0075-2 |
| [12] | P. Caputa et al., Anti-de Sitter space from optimization of path integrals in conformal field theories, Phys. Rev. Lett.119 (2017) 071602 [arXiv:1703.00456] [INSPIRE]. |
| [13] | R. Vasseur, A.C. Potter, Y.-Z. You and A.W.W. Ludwig, Entanglement transitions from holographic random tensor networks, Phys. Rev. B100 (2019) 134203 [arXiv:1807.07082] [INSPIRE]. |
| [14] | Hayden, P.; Penington, G., Learning the alpha-bits of black holes, JHEP, 12, 007 (2019) · Zbl 1431.83095 · doi:10.1007/JHEP12(2019)007 |
| [15] | Alexander, RN; Evenbly, G.; Klich, I., Exact holographic tensor networks for the Motzkin spin chain, Quantum, 5, 546 (2021) · doi:10.22331/q-2021-09-21-546 |
| [16] | Akers, C.; Faulkner, T.; Lin, S.; Rath, P., Reflected entropy in random tensor networks, JHEP, 05, 162 (2022) · Zbl 1522.81421 · doi:10.1007/JHEP05(2022)162 |
| [17] | N. Cheng et al., Random tensor networks with nontrivial links, arXiv:2206.10482 [INSPIRE]. |
| [18] | C. Akers, T. Faulkner, S. Lin and P. Rath, Reflected entropy in random tensor networks. Part II. A topological index from canonical purification, JHEP01 (2023) 067 [arXiv:2210.15006] [INSPIRE]. · Zbl 1540.83029 |
| [19] | A. Milekhin, P. Rath and W. Weng, Computable cross norm in tensor networks and holography, arXiv:2212.11978 [INSPIRE]. |
| [20] | L. Chen et al., Exact holographic tensor networks — constructing CFT_Dfrom TQFT_D+1, arXiv:2210.12127 [INSPIRE]. |
| [21] | Verlinde, E.; Verlinde, H., Black hole entanglement and quantum error correction, JHEP, 10, 107 (2013) · Zbl 1342.83211 · doi:10.1007/JHEP10(2013)107 |
| [22] | Almheiri, A.; Dong, X.; Harlow, D., Bulk locality and quantum error correction in AdS/CFT, JHEP, 04, 163 (2015) · Zbl 1388.81095 · doi:10.1007/JHEP04(2015)163 |
| [23] | Pastawski, F.; Yoshida, B.; Harlow, D.; Preskill, J., Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence, JHEP, 06, 149 (2015) · Zbl 1388.81094 · doi:10.1007/JHEP06(2015)149 |
| [24] | T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE]. |
| [25] | A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D74 (2006) 066009 [hep-th/0606141] [INSPIRE]. · Zbl 1165.81352 |
| [26] | D. Marolf and J. Polchinski, Gauge/gravity duality and the black hole interior, Phys. Rev. Lett.111 (2013) 171301 [arXiv:1307.4706] [INSPIRE]. |
| [27] | Chandra, J.; Collier, S.; Hartman, T.; Maloney, A., Semiclassical 3D gravity as an average of large-c CFTs, JHEP, 12, 069 (2022) · Zbl 1536.83053 · doi:10.1007/JHEP12(2022)069 |
| [28] | H. Verlinde, OPE and the BH information paradox, talk at the conference Gravitational emergence in AdS/CFT, video available at https://www.birs.ca, BIRS, October 2021. |
| [29] | H. Verlinde, On the quantum information content of a Hawking pair, arXiv:2210.08306 [INSPIRE]. |
| [30] | Goel, A.; Lam, HT; Turiaci, GJ; Verlinde, H., Expanding the black hole interior: partially entangled thermal states in SYK, JHEP, 02, 156 (2019) · Zbl 1411.83072 · doi:10.1007/JHEP02(2019)156 |
| [31] | H. Verlinde, On the quantum information content of a Hawking pair, arXiv:2210.08306 [INSPIRE]. |
| [32] | T. Hartman, Entanglement entropy at large central charge, arXiv:1303.6955 [INSPIRE]. |
| [33] | T. Faulkner, The entanglement Renyi entropies of disjoint intervals in AdS/CFT, arXiv:1303.7221 [INSPIRE]. |
| [34] | C. Akers et al., The black hole interior from non-isometric codes and complexity, arXiv:2207.06536 [INSPIRE]. |
| [35] | Penington, G.; Shenker, SH; Stanford, D.; Yang, Z., Replica wormholes and the black hole interior, JHEP, 03, 205 (2022) · Zbl 1522.83227 · doi:10.1007/JHEP03(2022)205 |
| [36] | Anous, T.; Hartman, T.; Rovai, A.; Sonner, J., Black hole collapse in the 1/c expansion, JHEP, 07, 123 (2016) · Zbl 1390.83170 · doi:10.1007/JHEP07(2016)123 |
| [37] | J. Chandra and T. Hartman, Coarse graining pure states in AdS/CFT, arXiv:2206.03414 [INSPIRE]. |
| [38] | Bah, I.; Chen, Y.; Maldacena, J., Estimating global charge violating amplitudes from wormholes, JHEP, 04, 061 (2023) · Zbl 07693949 · doi:10.1007/JHEP04(2023)061 |
| [39] | J.D. Brown and J.W. York Jr., Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D47 (1993) 1407 [gr-qc/9209012] [INSPIRE]. |
| [40] | Czech, B., A stereoscopic look into the bulk, JHEP, 07, 129 (2016) · Zbl 1390.83101 · doi:10.1007/JHEP07(2016)129 |
| [41] | Fitzpatrick, AL; Kaplan, J.; Li, D.; Wang, J., Exact Virasoro blocks from Wilson lines and background-independent operators, JHEP, 07, 092 (2017) · Zbl 1380.81314 · doi:10.1007/JHEP07(2017)092 |
| [42] | Cotler, J.; Jensen, K., AdS_3gravity and random CFT, JHEP, 04, 033 (2021) · Zbl 1462.83014 · doi:10.1007/JHEP04(2021)033 |
| [43] | A. Belin and J. de Boer, Random statistics of OPE coefficients and Euclidean wormholes, Class. Quant. Grav.38 (2021) 164001 [arXiv:2006.05499] [INSPIRE]. · Zbl 1482.81035 |
| [44] | Collier, S.; Gobeil, Y.; Maxfield, H.; Perlmutter, E., Quantum Regge trajectories and the Virasoro analytic bootstrap, JHEP, 05, 212 (2019) · Zbl 1416.81143 · doi:10.1007/JHEP05(2019)212 |
| [45] | Collier, S.; Maloney, A.; Maxfield, H.; Tsiares, I., Universal dynamics of heavy operators in CFT_2, JHEP, 07, 074 (2020) · Zbl 1451.81343 · doi:10.1007/JHEP07(2020)074 |
| [46] | Deutsch, JM, Quantum statistical mechanics in a closed system, Phys. Rev. A, 43, 2046 (1991) · doi:10.1103/PhysRevA.43.2046 |
| [47] | M. Srednicki, Chaos and quantum thermalization, cond-mat/9403051 [doi:10.1103/PhysRevE.50.888] [INSPIRE]. · Zbl 1113.81002 |
| [48] | N. Engelhardt and A.C. Wall, Decoding the apparent horizon: coarse-grained holographic entropy, Phys. Rev. Lett.121 (2018) 211301 [arXiv:1706.02038] [INSPIRE]. |
| [49] | Kar, A., Non-isometric quantum error correction in gravity, JHEP, 02, 195 (2023) · Zbl 1541.83050 · doi:10.1007/JHEP02(2023)195 |
| [50] | Anous, T.; Haehl, FM, On the Virasoro six-point identity block and chaos, JHEP, 08, 002 (2020) · Zbl 1454.81140 · doi:10.1007/JHEP08(2020)002 |
| [51] | H.W. Lin, J. Maldacena, L. Rozenberg and J. Shan, Holography for people with no time, arXiv:2207.00407 [INSPIRE]. |
| [52] | V. Balasubramanian et al., Multiboundary wormholes and holographic entanglement, Class. Quant. Grav.31 (2014) 185015 [arXiv:1406.2663] [INSPIRE]. · Zbl 1300.81067 |
| [53] | A. Peach and S.F. Ross, Tensor network models of multiboundary wormholes, Class. Quant. Grav.34 (2017) 105011 [arXiv:1702.05984] [INSPIRE]. · Zbl 1369.83097 |
| [54] | Maldacena, JM; Maoz, L., Wormholes in AdS, JHEP, 02, 053 (2004) · doi:10.1088/1126-6708/2004/02/053 |
| [55] | A. Maloney, Geometric microstates for the three dimensional black hole?, arXiv:1508.04079 [INSPIRE]. |
| [56] | Zamolodchikov, AB, Conformal symmetry in two-dimensional space: recursion representation of conformal block, Theor. Math. Phys., 73, 1088 (1987) · doi:10.1007/BF01022967 |
| [57] | Harlow, D.; Maltz, J.; Witten, E., Analytic continuation of Liouville theory, JHEP, 12, 071 (2011) · Zbl 1306.81287 · doi:10.1007/JHEP12(2011)071 |
| [58] | Brown, AR; Gharibyan, H.; Penington, G.; Susskind, L., The python’s lunch: geometric obstructions to decoding Hawking radiation, JHEP, 08, 121 (2020) · Zbl 1454.83046 · doi:10.1007/JHEP08(2020)121 |
| [59] | N. Seiberg, Notes on quantum Liouville theory and quantum gravity, Prog. Theor. Phys. Suppl.102 (1990) 319 [INSPIRE]. · Zbl 0790.53059 |
| [60] | D. Stanford, More quantum noise from wormholes, arXiv:2008.08570 [INSPIRE]. |
| [61] | P. Saad, Late time correlation functions, baby universes, and ETH in JT gravity, arXiv:1910.10311 [INSPIRE]. |
| [62] | H.W. Lin, J. Maldacena, L. Rozenberg and J. Shan, Looking at supersymmetric black holes for a very long time, arXiv:2207.00408 [INSPIRE]. |
| [63] | Sasieta, M., Wormholes from heavy operator statistics in AdS/CFT, JHEP, 03, 158 (2023) · Zbl 07690722 · doi:10.1007/JHEP03(2023)158 |
| [64] | Belin, A.; de Boer, J.; Liska, D., Non-Gaussianities in the statistical distribution of heavy OPE coefficients and wormholes, JHEP, 06, 116 (2022) · Zbl 1522.81452 · doi:10.1007/JHEP06(2022)116 |
| [65] | Dodelson, M.; Zhiboedov, A., Gravitational orbits, double-twist mirage, and many-body scars, JHEP, 12, 163 (2022) · Zbl 1536.83057 · doi:10.1007/JHEP12(2022)163 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
