Advertisement

Journal of High Energy Physics

, 2019:98 | Cite as

On volume subregion complexity in Vaidya spacetime

  • Roberto AuzziEmail author
  • Giuseppe Nardelli
  • Fidel I. Schaposnik Massolo
  • Gianni Tallarita
  • Nicolò Zenoni
Open Access
Regular Article - Theoretical Physics
  • 24 Downloads

Abstract

We study holographic subregion volume complexity for a line segment in the AdS3 Vaidya geometry. On the field theory side, this gravity background corresponds to a sudden quench which leads to the thermalization of the strongly-coupled dual conformal field theory. We find the time-dependent extremal volume surface by numerically solving a partial differential equation with boundary condition given by the Hubeny-Rangamani- Takayanagi surface, and we use this solution to compute holographic subregion complexity as a function of time. Approximate analytical expressions valid at early and at late times are derived.

Keywords

AdS-CFT Correspondence Black Holes 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

References

  1. [1]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96 (2006) 181602 [hep-th/0603001] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  2. [2]
    H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP05 (2011) 036 [arXiv:1102.0440] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  3. [3]
    A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP08 (2013) 090 [arXiv:1304.4926] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  4. [4]
    J.D. Bekenstein, Black holes and entropy, Phys. Rev.D 7 (1973) 2333 [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  5. [5]
    L. Susskind, Computational complexity and black hole horizons, Fortsch. Phys.64 (2016) 44 [arXiv:1403.5695] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  6. [6]
    D. Stanford and L. Susskind, Complexity and shock wave geometries, Phys. Rev.D 90 (2014) 126007 [arXiv:1406.2678] [INSPIRE].ADSGoogle Scholar
  7. [7]
    L. Susskind, Entanglement is not enough, Fortsch. Phys.64 (2016) 49 [arXiv:1411.0690] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  8. [8]
    M.A. Nielsen, A geometric approach to quantum circuit lower bounds, Quant. Inf. Comput.6 (2006) 213 [quant-ph/0502070].
  9. [9]
    M.R. Dowling and M.A. Nielsen, The geometry of quantum computation, Quant. Inf. Comput.8 (2008) 861 [quant-ph/0701004].
  10. [10]
    R. Jefferson and R.C. Myers, Circuit complexity in quantum field theory, JHEP10 (2017) 107 [arXiv:1707.08570] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  11. [11]
    S. Chapman, M.P. Heller, H. Marrochio and F. Pastawski, Toward a definition of complexity for quantum field theory states, Phys. Rev. Lett.120 (2018) 121602 [arXiv:1707.08582] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  12. [12]
    K. Hashimoto, N. Iizuka and S. Sugishita, Time evolution of complexity in Abelian gauge theories, Phys. Rev.D 96 (2017) 126001 [arXiv:1707.03840] [INSPIRE].ADSMathSciNetGoogle Scholar
  13. [13]
    P. Caputa et al., Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT, JHEP11 (2017) 097 [arXiv:1706.07056] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  14. [14]
    A. Bhattacharyya et al., Path-integral complexity for perturbed CFTs, JHEP07 (2018) 086 [arXiv:1804.01999] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  15. [15]
    S. Chapman et al., Complexity and entanglement for thermofield double states, SciPost Phys.6 (2019) 034 [arXiv:1810.05151] [INSPIRE].CrossRefADSGoogle Scholar
  16. [16]
    A.R. Brown et al., Holographic complexity equals bulk action?, Phys. Rev. Lett.116 (2016) 191301 [arXiv:1509.07876] [INSPIRE].CrossRefADSGoogle Scholar
  17. [17]
    A.R. Brown et al., Complexity, action and black holes, Phys. Rev.D 93 (2016) 086006 [arXiv:1512.04993] [INSPIRE].
  18. [18]
    L. Lehner, R.C. Myers, E. Poisson and R.D. Sorkin, Gravitational action with null boundaries, Phys. Rev.D 94 (2016) 084046 [arXiv:1609.00207] [INSPIRE].
  19. [19]
    R.-G. Cai et al., Action growth for AdS black holes, JHEP09 (2016) 161 [arXiv:1606.08307] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  20. [20]
    S. Chapman, H. Marrochio and R.C. Myers, Complexity of formation in holography, JHEP01 (2017) 062 [arXiv:1610.08063] [INSPIRE].
  21. [21]
    D. Carmi et al., On the time dependence of holographic complexity, JHEP11 (2017) 188 [arXiv:1709.10184] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  22. [22]
    M. Alishahiha, A. Faraji Astaneh, A. Naseh and M.H. Vahidinia, On complexity for F (R) and critical gravity, JHEP05 (2017) 009 [arXiv:1702.06796] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  23. [23]
    M. Ghodrati, Complexity growth in massive gravity theories, the effects of chirality and more, Phys. Rev.D 96 (2017) 106020 [arXiv:1708.07981] [INSPIRE].ADSMathSciNetGoogle Scholar
  24. [24]
    R. Auzzi, S. Baiguera and G. Nardelli, Volume and complexity for warped AdS black holes, JHEP06 (2018) 063 [arXiv:1804.07521] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  25. [25]
    R. Auzzi et al., Complexity and action for warped AdS black holes, JHEP09 (2018) 013 [arXiv:1806.06216] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  26. [26]
    H. Dimov, R.C. Rashkov and T. Vetsov, Thermodynamic information geometry and complexity growth of a warped AdS black hole and the warped AdS 3/CFT 2correspondence, Phys. Rev.D 99 (2019) 126007 [arXiv:1902.02433] [INSPIRE].ADSGoogle Scholar
  27. [27]
    M. Alishahiha, A. Faraji Astaneh, M.R. Mohammadi Mozaffar and A. Mollabashi, Complexity growth with Lifshitz scaling and hyperscaling violation, JHEP07 (2018) 042 [arXiv:1802.06740] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  28. [28]
    M. Flory and N. Miekley, Complexity change under conformal transformations in AdS 3/CFT 2 , JHEP05 (2019) 003 [arXiv:1806.08376] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  29. [29]
    M. Flory, WdW-patches in AdS 3and complexity change under conformal transformations II, JHEP05 (2019) 086 [arXiv:1902.06499] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  30. [30]
    V. Balasubramanian et al., Holographic Thermalization, Phys. Rev.D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
  31. [31]
    M. Moosa, Evolution of complexity following a global quench, JHEP03 (2018) 031 [arXiv:1711.02668] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  32. [32]
    M. Moosa, Divergences in the rate of complexification, Phys. Rev.D 97 (2018) 106016 [arXiv:1712.07137] [INSPIRE].ADSMathSciNetGoogle Scholar
  33. [33]
    S. Chapman, H. Marrochio and R.C. Myers, Holographic complexity in Vaidya spacetimes. Part I, JHEP06 (2018) 046 [arXiv:1804.07410] [INSPIRE].
  34. [34]
    S. Chapman, H. Marrochio and R.C. Myers, Holographic complexity in Vaidya spacetimes. Part II, JHEP06 (2018) 114 [arXiv:1805.07262] [INSPIRE].
  35. [35]
    M. Nozaki, T. Numasawa and T. Takayanagi, Holographic local quenches and entanglement density, JHEP05 (2013) 080 [arXiv:1302.5703] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  36. [36]
    D.S. Ageev, I.Ya. Aref’eva, A.A. Bagrov and M.I. Katsnelson, Holographic local quench and effective complexity, JHEP08 (2018) 071 [arXiv:1803.11162] [INSPIRE].
  37. [37]
    D. Ageev, Holographic complexity of local quench at finite temperature, arXiv:1902.03632 [INSPIRE].
  38. [38]
    B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, The gravity dual of a density matrix, Class. Quant. Grav.29 (2012) 155009 [arXiv:1204.1330] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  39. [39]
    V.E. Hubeny and M. Rangamani, Causal holographic information, JHEP06 (2012) 114 [arXiv:1204.1698] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  40. [40]
    M. Alishahiha, Holographic complexity, Phys. Rev.D 92 (2015) 126009 [arXiv:1509.06614] [INSPIRE].ADSMathSciNetGoogle Scholar
  41. [41]
    D. Carmi, R.C. Myers and P. Rath, Comments on holographic complexity, JHEP03 (2017) 118 [arXiv:1612.00433] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  42. [42]
    V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP07 (2007) 062 [arXiv:0705.0016] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  43. [43]
    C.A. Agón, M. Headrick and B. Swingle, Subsystem complexity and holography, JHEP02 (2019) 145 [arXiv:1804.01561] [INSPIRE].
  44. [44]
    E. Cáceres, J. Couch, S. Eccles and W. Fischler, Holographic purification complexity, Phys. Rev.D 99 (2019) 086016 [arXiv:1811.10650] [INSPIRE].
  45. [45]
    O. Ben-Ami and D. Carmi, On volumes of subregions in holography and complexity, JHEP11 (2016) 129 [arXiv:1609.02514] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  46. [46]
    R. Abt et al., Topological complexity in AdS 3/CFT 2 , Fortsch. Phys.66 (2018) 1800034 [arXiv:1710.01327] [INSPIRE].CrossRefMathSciNetGoogle Scholar
  47. [47]
    R. Abt et al., Holographic subregion complexity from kinematic space, JHEP01 (2019) 012 [arXiv:1805.10298] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  48. [48]
    M. Alishahiha, K. Babaei Velni and M.R. Mohammadi Mozaffar, Black hole subregion action and complexity, Phys. Rev.D 99 (2019) 126016 [arXiv:1809.06031] [INSPIRE].ADSGoogle Scholar
  49. [49]
    P. Roy and T. Sarkar, Note on subregion holographic complexity, Phys. Rev.D 96 (2017) 026022 [arXiv:1701.05489] [INSPIRE].
  50. [50]
    P. Roy and T. Sarkar, Subregion holographic complexity and renormalization group flows, Phys. Rev.D 97 (2018) 086018 [arXiv:1708.05313] [INSPIRE].
  51. [51]
    E. Bakhshaei, A. Mollabashi and A. Shirzad, Holographic subregion complexity for singular surfaces, Eur. Phys. J.C 77 (2017) 665 [arXiv:1703.03469] [INSPIRE].CrossRefADSGoogle Scholar
  52. [52]
    A. Bhattacharya, K.T. Grosvenor and S. Roy, Entanglement entropy and subregion complexity in thermal perturbations around pure-AdS, arXiv:1905.02220 [INSPIRE].
  53. [53]
    R. Auzzi, S. Baiguera, A. Mitra, G. Nardelli and N. Zenoni, Subsystem complexity in warped AdS, JHEP09 (2019) 114 [arXiv:1906.09345] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  54. [54]
    B. Chen et al., Holographic subregion complexity under a thermal quench, JHEP07 (2018) 034 [arXiv:1803.06680] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  55. [55]
    Y. Ling, Y. Liu and C.-Y. Zhang, Holographic subregion complexity in Einstein-Born-Infeld theory, Eur. Phys. J.C 79 (2019) 194 [arXiv:1808.10169] [INSPIRE].CrossRefADSGoogle Scholar
  56. [56]
    Y.-T. Zhou, M. Ghodrati, X.-M. Kuang and J.-P. Wu, Evolutions of entanglement and complexity after a thermal quench in massive gravity theory, Phys. Rev.D 100 (2019) 066003 [arXiv:1907.08453] [INSPIRE].
  57. [57]
    Y. Ling et al., Holographic subregion complexity in general Vaidya geometry, JHEP11 (2019) 039 [arXiv:1908.06432] [INSPIRE].CrossRefGoogle Scholar
  58. [58]
    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].
  59. [59]
    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].
  60. [60]
    S. Chapman, D. Ge and G. Policastro, Holographic complexity for defects distinguishes action from volume, JHEP05 (2019) 049 [arXiv:1811.12549] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  61. [61]
    D.W.F. Alves and G. Camilo, Evolution of complexity following a quantum quench in free field theory, JHEP06 (2018) 029 [arXiv:1804.00107] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  62. [62]
    H.A. Camargo et al., Complexity as a novel probe of quantum quenches: universal scalings and purifications, Phys. Rev. Lett.122 (2019) 081601 [arXiv:1807.07075] [INSPIRE].
  63. [63]
    S. Lloyd, Ultimate physical limits to computation, Nature406 (2000) 1047.CrossRefADSGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica e FisicaUniversità Cattolica del Sacro CuoreBresciaItaly
  2. 2.INFN — Sezione di PerugiaPerugiaItaly
  3. 3.TIFPA — INFN, c/o Dipartimento di FisicaUniversità di TrentoPovoItaly
  4. 4.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance
  5. 5.Departamento de Ciencias, Facultad de Artes LiberalesUniversidad Adolfo IbáñezSantiagoChile
  6. 6.Instituut voor Theoretische FysicaKU LeuvenLeuvenBelgium

Personalised recommendations