Holographic complexity under a global quantum quench

Fan, Zhong-Ying; Guo, Minyong

doi:10.1016/j.nuclphysb.2019.114818

Cited by 27 publications

(16 citation statements)

References 111 publications

(178 reference statements)

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“…In the AdS/CFT correspondence, there are two popular proposals for complexity, usually dubbed by "Complexity=Volume" (CV) duality [7,8] and "Complex-ity=Action" (CA) duality [9,10]. The two conjectures have been extensively studied in literature [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46]. However, there are some drawbacks for the two proposals as well.…”

Section: Introductionmentioning

confidence: 99%

“…Here ct is an arbitrary length scale, Θ is the scalar expansion defined by Θ = ∇ µ k µ andΘ = ∇ µ sk µ . Though the inclusion of this counter term is not necessary for the action principle, it plays an indispensable role in shockwave geometries [18,19,20,21] as well as in other time dependent geometries [22]. However, for static black holes it does not have any time dependence and hence is irrelevant to current paper.…”

Section: Introductionmentioning

confidence: 99%

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Time dependence of complexity for Lovelock black holes

Fan

Liang

2019

Phys. Rev. D

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We study the general time dependence of complexity for holographic states dual to Lovelock black holes using the "Complexity=Action" (CA) proposal. We observe that at early times, the critical time at which the complexity begins to increase is a decreasing function of the higher order coupling constants, which implies that the complexity evolves faster than that of Schwarzschild black holes. At late times, the rate of change of complexity is essentially determined by the generalised Gibbons-Hawking-York boundary term evaluated at the future singularity. In particular, its ratio to black hole mass is a characteristic constant, independent of the higher order couplings. Thus, in the vanishing coupling limit, the result in general does not reduce to that of Schwarzschild black holes, in spite of that the metric reduces to the latter as well as the gravitational action. In fact, the two differ by a constant during the whole time evolution. Including the next-to-leading order term around late times, we find that as the Einstein case, the late time limit is always approached from above, thus violating any conjectured upper bound given by the late time result. For charged Lovelock black holes, we find that with sufficient charge, the complexity roughly behaves the same as the Einstein case. However, for smaller charges, the two have some significant differences. In particular, unlike the Einstein case, in the uncharged limit the complexity growth rate does not match with the neutral case, differing by a constant in the whole time evolution.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time dependence of complexity for Lovelock black holes

Fan

Liang

2019

Phys. Rev. D

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“…On the other hand, recent developments in AdS/CFT correspondence give rise to several distinct proposals for complexity for a holographic state [4,5,6,8,9]. However, though these proposals show interesting properties of complexity and have attracted a lot of attentions in literature [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,32,33,34,35,36,37,38,39,40], none of them obeys the Lloyd bound for general holographic theories.…”

Section: Introductionmentioning

confidence: 99%

Holographic complexity and thermodynamics of AdS black holes

Fan

Guo

2019

Phys. Rev. D

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In this paper, we relate the complexity for a holographic state to a simple gravitational object of which the growth rate at late times is equal to temperature times black hole entropy. We show that if this is correct, the thermodynamics of AdS black holes implies that for generic holographic states dual to static AdS black holes, the complexity growth rate at late times will saturate the Lloyd bound at high temperature limit. In particular, for AdS planar black holes, the result holds at lower temperatures as well. We conjecture that the complexity growth is bounded above as dC/dt ≤ αT S/π or dC/dt ≤ α T + S + − T − S − /π for black holes with an inner horizon, where α is an overall coefficient for our new proposal.The conjecture passes a number of nontrivial tests for black holes in Einstein's gravity.However, we also find that the bound may be violated in the presence of stringy corrections.

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“…The holographic dual of this process is given by the Vaidya geometry, which is equipped with a thin shell of null fluid collapse (shockwave) [82][83][84][85][86][87][88][89]. Based on this duality, the time-dependence of the complexity in the boundary quantum field system has been studied by using different holographic complexities [65][66][67][68][69][70][71][72].…”

Section: Introductionmentioning

confidence: 99%

Switchback effect of holographic complexity in multiple-horizon black holes

2020

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In this paper, we use the "complexity equals action" (CA) conjecture to explore the switchback effect in the strongly-coupled quantum field theories with finite N and finite coupling effects. In the perspective of holography, this is equivalent to evaluating the CA complexity in a Vaidya geometry equipped with a light shockwave for a higher curvature gravitational theory. Based on the Noether charge formalism of Iyer and Wald, we obtain the slope of the complexity of formation in the small and large time approximations. By circuit analogy, we show that our results concur with the switchback effect of the quantum system. These results show that the switchback effect is a general feature of the CA complexity in stationary black holes and its existence is independent of the explicit gravitational theory as well as spacetime background. From the viewpoint of AdS/CFT, this also implies that the switchback effect is a general feature of the thermofield double state in the strongly-coupled quantum field systems with finite N and finite coupling effects. Moreover, we also illustrate that unlike the late-time complexity growth rate, the counterterm plays an important role in the study of the switchback effect.

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Holographic complexity under a global quantum quench

Cited by 27 publications

References 111 publications

Time dependence of complexity for Lovelock black holes

Time dependence of complexity for Lovelock black holes

Holographic complexity and thermodynamics of AdS black holes

Switchback effect of holographic complexity in multiple-horizon black holes

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