Lorentzian threads and generalized complexity. (English) Zbl 07865580
Summary: Recently, an infinite class of holographic generalized complexities was proposed. These gravitational observables display the behavior required to be duals of complexity, in particular, linear growth at late times and switchback effect. In this work, we aim to understand generalized complexities in the framework of Lorentzian threads. We reformulate the problem in terms of thread distributions and measures and present a program to calculate the infinite family of codimension-one observables. We also outline a path to understand, using threads, the more subtle case of codimension-zero observables.
MSC:
| 81-XX | Quantum theory |
References:
| [1] | Freedman, M.; Headrick, M., Bit threads and holographic entanglement, Commun. Math. Phys., 352, 407, 2017 · Zbl 1425.81014 · doi:10.1007/s00220-016-2796-3 |
| [2] | Harper, J.; Headrick, M., Bit threads and holographic entanglement of purification, JHEP, 08, 101, 2019 · Zbl 1421.83101 · doi:10.1007/JHEP08(2019)101 |
| [3] | Bao, N.; Halpern, IF, Holographic Inequalities and Entanglement of Purification, JHEP, 03, 006, 2018 · Zbl 1388.81626 · doi:10.1007/JHEP03(2018)006 |
| [4] | Hubeny, VE, Bulk locality and cooperative flows, JHEP, 12, 068, 2018 · Zbl 1405.81133 · doi:10.1007/JHEP12(2018)068 |
| [5] | Agón, CA; De Boer, J.; Pedraza, JF, Geometric Aspects of Holographic Bit Threads, JHEP, 05, 075, 2019 · Zbl 1416.83094 · doi:10.1007/JHEP05(2019)075 |
| [6] | Cui, SX, Bit Threads and Holographic Monogamy, Commun. Math. Phys., 376, 609, 2019 · Zbl 1476.81012 · doi:10.1007/s00220-019-03510-8 |
| [7] | Agón, CA; Pedraza, JF, Quantum bit threads and holographic entanglement, JHEP, 02, 180, 2022 · Zbl 1522.81026 · doi:10.1007/JHEP02(2022)180 |
| [8] | N. Bao and J. Harper, Bit threads on hypergraphs, arXiv:2012.07872 [INSPIRE]. |
| [9] | Agón, CA; Cáceres, E.; Pedraza, JF, Bit threads, Einstein’s equations and bulk locality, JHEP, 01, 193, 2021 · Zbl 1459.83003 |
| [10] | Gürsoy, U.; Pedraza, JF; Planas, GP, Holographic entanglement as nonlocal magnetism, JHEP, 09, 091, 2023 · Zbl 07754670 · doi:10.1007/JHEP09(2023)091 |
| [11] | Pedraza, JF; Russo, A.; Svesko, A.; Weller-Davies, Z., Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity, JHEP, 02, 093, 2022 · Zbl 1522.83304 · doi:10.1007/JHEP02(2022)093 |
| [12] | Susskind, L., Entanglement is not enough, Fortsch. Phys., 64, 49, 2016 · Zbl 1429.81021 · doi:10.1002/prop.201500095 |
| [13] | Susskind, L., Computational Complexity and Black Hole Horizons, Fortsch. Phys., 64, 24, 2016 · Zbl 1429.81019 · doi:10.1002/prop.201500092 |
| [14] | L. Susskind and Y. Zhao, Switchbacks and the Bridge to Nowhere, arXiv:1408.2823 [INSPIRE]. |
| [15] | Brown, AR, Holographic Complexity Equals Bulk Action?, Phys. Rev. Lett., 116, 2016 · doi:10.1103/PhysRevLett.116.191301 |
| [16] | Brown, AR, Complexity, action, and black holes, Phys. Rev. D, 93, 2016 · doi:10.1103/PhysRevD.93.086006 |
| [17] | Headrick, M.; Hubeny, VE, Riemannian and Lorentzian flow-cut theorems, Class. Quant. Grav., 35, 10, 2018 · Zbl 1391.83016 · doi:10.1088/1361-6382/aab83c |
| [18] | Pedraza, JF; Russo, A.; Svesko, A.; Weller-Davies, Z., Lorentzian Threads as Gatelines and Holographic Complexity, Phys. Rev. Lett., 127, 2021 · doi:10.1103/PhysRevLett.127.271602 |
| [19] | Belin, A., Does Complexity Equal Anything?, Phys. Rev. Lett., 128, 2022 · doi:10.1103/PhysRevLett.128.081602 |
| [20] | Belin, A., Complexity equals anything II, JHEP, 01, 154, 2023 · Zbl 1540.83037 · doi:10.1007/JHEP01(2023)154 |
| [21] | Couch, J.; Fischler, W.; Nguyen, PH, Noether charge, black hole volume, and complexity, JHEP, 03, 119, 2017 · Zbl 1377.83039 · doi:10.1007/JHEP03(2017)119 |
| [22] | K.P.S. Bhaskara Rao and M. Bhaskara Rao, Theory of charges: a study of finitely additive measures, Academic Press (1983). · Zbl 0516.28001 |
| [23] | Headrick, M.; Hubeny, VE, Covariant bit threads, JHEP, 07, 180, 2023 · Zbl 07744325 · doi:10.1007/JHEP07(2023)180 |
| [24] | Boyd, S.; Vandenberghe, L., Convex Optimization, Cambridge University Press, 2004 · Zbl 1058.90049 · doi:10.1017/cbo9780511804441 |
| [25] | Treude, J-H; Grant, JDE, Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems, Ann. Glob. Anal. Geom., 43, 233, 2013 · Zbl 1268.53076 · doi:10.1007/s10455-012-9343-z |
| [26] | Chandra, AR, Cost of holographic path integrals, SciPost Phys., 14, 061, 2023 · Zbl 07901915 · doi:10.21468/SciPostPhys.14.4.061 |
| [27] | Marsden, JE; Tipler, FJ, Maximal hypersurfaces and foliations of constant mean curvature in general relativity, Phys. Rept., 66, 109, 1980 · doi:10.1016/0370-1573(80)90154-4 |
| [28] | Pedraza, JF; Russo, A.; Svesko, A.; Weller-Davies, Z., Computing spacetime, Int. J. Mod. Phys. D, 31, 2242010, 2022 · doi:10.1142/S021827182242010X |
| [29] | Carrasco, R.; Pedraza, JF; Svesko, A.; Weller-Davies, Z., Gravitation from optimized computation: Einstein and beyond, JHEP, 09, 167, 2023 · Zbl 07754746 · doi:10.1007/JHEP09(2023)167 |
| [30] | E. Cáceres et al., Einstein’s equations and generalized complexities, work in progress. |
| [31] | S.E. Aguilar-Gutierrez, M.P. Heller and S. Van der Schueren, Complexity = Anything Can Grow Forever in de Sitter, arXiv:2305.11280 [INSPIRE]. |
| [32] | Jørstad, E.; Myers, RC; Ruan, S-M, Complexity = anything: singularity probes, JHEP, 07, 223, 2023 · Zbl 07744368 · doi:10.1007/JHEP07(2023)223 |
| [33] | Feng, JC; Matzner, RA, The Weiss Variation of the Gravitational Action, Gen. Rel. Grav., 50, 99, 2018 · Zbl 1400.83004 · doi:10.1007/s10714-018-2420-2 |
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