On the time dependence of holographic complexity

Dean Carmi, Shira Chapman, Hugo Marrochio, Robert C. Myers, Sotaro Sugishita

Research output: Contribution to journalArticlepeer-review


We evaluate the full time dependence of holographic complexity in various eternal black hole backgrounds using both the complexity=action (CA) and the complexity=volume (CV) conjectures. We conclude using the CV conjecture that the rate of change of complexity is a monotonically increasing function of time, which saturates from below to a positive constant in the late time limit. Using the CA conjecture for uncharged black holes, the holographic complexity remains constant for an initial period, then briefly decreases but quickly begins to increase. As observed previously, at late times, the rate of growth of the complexity approaches a constant, which may be associated with Lloyd’s bound on the rate of computation. However, we find that this late time limit is approached from above, thus violating the bound. For either conjecture, we find that the late time limit for the rate of change of complexity is saturated at times of the order of the inverse temperature. Adding a charge to the eternal black holes washes out the early time behaviour, i.e. complexity immediately begins increasing with sufficient charge, but the late time behaviour is essentially the same as in the neutral case. We also evaluate the complexity of formation for charged black holes and find that it is divergent for extremal black holes, implying that the states at finite chemical potential and zero temperature are infinitely more complex than their finite temperature counterparts.

Original languageEnglish
Article number188
JournalJournal of High Energy Physics
Issue number11
StatePublished - 1 Nov 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017, The Author(s).


  • AdS-CFT Correspondence
  • Black Holes
  • Gauge-gravity correspondence

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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