Complexity growth and shock wave geometry in AdS-Maxwell-power-Yang–Mills theory

Yaraie, Emad; Ghaffarnejad, Hossein; Farsam, Mohammad

doi:10.1140/epjc/s10052-018-6456-y

Cited by 25 publications

(15 citation statements)

References 27 publications

(53 reference statements)

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“…We numerically solve above equations for the HRT surface γ A and denote the solutions as (ṽ(x),z(x)), then the equation in (21) becomes…”

Section: Holographic Entanglement Entropymentioning

confidence: 99%

“…Once we figure out the HRT surface, the corresponding HEE can be obtained from equation (21). Since we are only concerned with the change of the HEE during the quench, we may subtract the vacuum HEE and define a finite quantity for HEE as…”

Section: The Evolution Of Subregion Complexitymentioning

confidence: 99%

“…See the generalizations of the conjectures to CV 2.0 and CA2.0 in [17][18][19]. Others see [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

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Holographic subregion complexity in Einstein-Born-Infeld theory

2019

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We numerically investigate the evolution of the holographic subregion complexity during a quench process in Einstein-Born-Infeld theory. Based on the subregion CV conjecture, we argue that the subregion complexity can be treated as a probe to explore the interior of the black hole. The effects of the nonlinear parameter and the charge on the evolution of the holographic subregion complexity are also investigated. When the charge is sufficiently large, it not only changes the evolution pattern of the subregion complexity, but also washes out the second stage featured by linear growth.

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“…We numerically solve above equations for the HRT surface γ A and denote the solutions as (ṽ(x),z(x)), then the equation in (21) becomes…”

Section: Holographic Entanglement Entropymentioning

confidence: 99%

Section: The Evolution Of Subregion Complexitymentioning

confidence: 99%

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Holographic subregion complexity in Einstein-Born-Infeld theory

2019

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“…One is the "complexity = volume" (CV) conjecture [5,6] and the other is the "complexity = action" (CA) conjecture [7,8]. These conjectures attracted considerable attentions and many works have been done to investigate the properties of holographic complexity associated with these two conjectures [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and to further generalize these two conjectures [29,30,[32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Holographic complexity bounds

Liu

Lü

et al. 2020

J. High Energ. Phys.

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We study the action growth rate in the Wheeler-DeWitt (WDW) patch for a variety of D ≥ 4 black holes in Einstein gravity that are asymptotic to the anti-de Sitter spacetime, with spherical, toric and hyperbolic horizons, corresponding to the topological parameter k = 1, 0, −1 respectively. We find a lower bound inequality 1 T ∂İ WDW ∂S Q,P th > C for k = 0, 1, where C is some order-one numerical constant. The lowest number in our examples is C = (D − 3)/(D − 2). We also find that the quantity (İ WDW − 2P th ∆V th) is greater than, equal to, or less than zero, for k = 1, 0, −1 respectively. For black holes with two horizons, ∆V th = V + th − V − th , i.e. the difference between the thermodynamical volumes of the outer and inner horizons. For black holes with only one horizon, we introduce a new concept of the volume V 0 th of the black hole singularity, and define ∆V th = V + th − V 0 th. The volume V 0 th vanishes for the Schwarzschild black hole, but in general it can be positive, negative or even divergent. For black holes with single horizon, we find a relation betweeṅ I WDW and V 0 th , which implies that the holographic complexity preserves the Lloyd's bound for positive or vanishing V 0 th , but the bound is violated when V 0 th becomes negative. We also find explicit black hole examples where V 0 th and henceİ WDW are divergent.

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“…Recently, two proposals about quantum computational complexity have emerged, namely, the conjecture of complexity = volume (CV) [9,10] and the conjecture of complexity = action (CA) [11,12]. Many studies has been done about these two conjectures, see [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and references there in. In this paper, we shall follow the CA conjecture.…”

Section: Introductionmentioning

confidence: 99%

Holographic complexity growth rate in Horndeski theory

Feng

Liu

2019

Eur. Phys. J. C

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Based on the context of complexity = action (CA) conjecture, we calculate the holographic complexity of AdS black holes with planar and spherical topologies in Horndeski theory. We find that the rate of change of holographic complexity for neutral AdS black holes saturates the Lloyd's bound. For charged black holes, we find that there exists only one horizon and thus the corresponding holographic complexity can't be expressed as the difference of some thermodynamical potential between two horizons as that of Reissner-Nordstrom AdS black hole in Einstein-Maxwell theory. However, the Lloyd's bound is not violated for charged AdS black hole in Horndeski theory.

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Complexity growth and shock wave geometry in AdS-Maxwell-power-Yang–Mills theory

Cited by 25 publications

References 27 publications

Holographic subregion complexity in Einstein-Born-Infeld theory

Holographic subregion complexity in Einstein-Born-Infeld theory

Holographic complexity bounds

Holographic complexity growth rate in Horndeski theory

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