Phys. Rev. D
 2016
DOI: 10.1103/physrevd.93.086006
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Complexity, action, and black holes

Adam R. Brown
1
,
Daniel A. Roberts
2
,
Leonard Susskind
3
et al.

Abstract: Our earlier paper "Complexity Equals Action" conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the 'Wheeler-DeWitt' patch). We provide calculations for the results quoted in that paper; explain how it fits into a broader (tensor) network of ideas; and elaborate on the hypothesis that black holes are fastest computers in nature.

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Cited by 744 publications

(1,398 citation statements)
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“…This conclusion agrees with the one from the CA conjecture [31], and it is also expected from the field theory side considering the Gauss-Bonnet term as some correction of large N expansion [81]. In particular, it is speculated that stringy corrections should reduce the complexity growth rate of the AdS black hole solutions [15].…”
Section: A Summary Of Our Resultssupporting
confidence: 88%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
show abstract
“…This conclusion agrees with the one from the CA conjecture [31], and it is also expected from the field theory side considering the Gauss-Bonnet term as some correction of large N expansion [81]. In particular, it is speculated that stringy corrections should reduce the complexity growth rate of the AdS black hole solutions [15].…”
Section: A Summary Of Our Resultssupporting
confidence: 88%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
show abstract
“…21 Therefore dC A /dt 0 is monotonically increasing and approaches the late time limit from below. These features contrast with the corresponding results for the eternal black hole [46], and as previously noted in [47], for the process of black hole formation, dC A /dt 0 respects the proposed bound on the rate of complexity growth suggested in [29,30], i.e., dC A /dt 0 ≤ 2M/π.…”
Section: Time Dependence Of Complexity Versioncontrasting
confidence: 99%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
show abstract
“…In the case of solutions with constant Ricci curvature, we have confirmed the results of Refs. [5,6], namely the action growth corresponds to the double of the Killing energy, in agreement with the result of Brown et al in General Relativity [2]. On the other hand, for solutions with non-constant Ricci curvature, the Kodama-Hayward BH energy emerges in the action growth.…”
Section: Discussionsupporting
confidence: 89%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
show abstract
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