Complexity growth in flat spacetimes

Fareghbal, Reza; Karimi, Pedram

doi:10.1103/physrevd.98.046003

Cited by 17 publications

(9 citation statements)

References 67 publications

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“…Our main concern was to compute finite term of the on-shell action. It is contrary to the most studies in the literature where the main concern was to compute the growth rate of the complexity (see for example [53][54][55][56][57][58][59][60][61][62][63][64][65][66]).…”

Section: Discussionmentioning

confidence: 92%

Black hole subregion action and complexity

2019

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We evaluate finite part of the on-shell action for black brane solutions of Einstein gravity on different subregions of spacetime enclosed by null boundaries. These subregions include the intersection of WDW patch with past/future interior and left/right exterior for a two sided black brane. Identifying the on-shell action on the exterior regions with subregion complexity one finds that it obeys subadditivity condition. This gives an insight to define a new quantity named mutual complexity. We will also consider certain subregion that is a part of spacetime which could be causally connected to an operator localized behind/outside the horizon. Taking into account all terms needed to have a diffeomorphism invariant action with a well-defined variational principle, one observes that the main contribution that results to a nontrivial behavior of the onshell action comes from joint points where two lightlike boundaries (including horizon) intersect. A spacelike boundary gives rise to a linear time growth, while we have a classical contribution due to a timelike boundary that is given by the free energy.

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Section: Discussionmentioning

confidence: 92%

Black hole subregion action and complexity

2019

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“…Despite this change, and since JHEP02(2022)093 holographic complexity conjectures have not been systematically derived from fundamental principles of AdS/CFT, it is natural to propose holographic complexity, specifically CV duality, holds in these other spacetimes. The complexity=action conjecture was previously considered to hold for flat spacetimes in [180], while both CV and CA proposals have been analyzed in de Sitter space [181]; de Sitter space even has a tensor network description [182]. It would be interesting to further investigate Lorentzian flows in these spacetimes and extend the gateline picture developed here accordingly.…”

Section: Jhep02(2022)093mentioning

confidence: 89%

Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity

Pedraza

Russo

Svesko

et al. 2022

J. High Energ. Phys.

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Holographic entanglement entropy was recently recast in terms of Riemannian flows or ‘bit threads’. We consider the Lorentzian analog to reformulate the ‘complexity=volume’ conjecture using Lorentzian flows — timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. By the nesting of Lorentzian flows, holographic complexity is shown to obey a number of properties. Particularly, the rate of complexity is bounded below by conditional complexity, describing a multi-step optimization with intermediate and final target states. We provide multiple explicit geometric realizations of Lorentzian flows in AdS backgrounds, including their time-dependence and behavior near the singularity in a black hole interior. Conceptually, discretized flows are interpreted as Lorentzian threads or ‘gatelines’. Upon selecting a reference state, complexity thence counts the minimum number of gatelines needed to prepare a target state described by a tensor network discretizing the maximal volume slice, matching its quantum information theoretic definition. We point out that suboptimal tensor networks are important to fully characterize the state, leading us to propose a refined notion of complexity as an ensemble average. The bulk symplectic potential provides a specific ‘canonical’ thread configuration characterizing perturbations around arbitrary CFT states. Consistency of this solution requires the bulk satisfy the linearized Einstein’s equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating for a principle of ‘spacetime complexity’. Lastly, we argue Lorentzian threads provide a notion of emergent time. This article is an expanded and detailed version of [1], including several new results.

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“…Inspired by the Hubney-Ryu-Takayanagi proposal, the CV proposal extends to be defined on subregions corresponding to the complexity of mixed states, which is known as holographic subregion complexity (HSC), in which the complexity of a subsystem on the boundary equals the volume of codimensional-one hypersurface enclosed by Hubney-Ryu-Takayanagi surface [11]. There are a lot of works on CV, CA and HSC for various gravity models in the literature [12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Note on stability and holographic subregion complexity

Ali-Akbari

Lezgi

2022

Eur. Phys. J. C

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We study holographic subregion complexity in a spatially anisotropic field theory, which expresses a confinement-deconfinement phase transition. Its holographic dual is a five-dimensional anisotropic holographic model characterized by a Van der Waals-like phase transition between small and large black holes. We propose a new interpretation from the informational perspective to determine the stable and unstable thermodynamically solutions. According to this proposal, the states which need (more) less information to be specified characterize the (un) stable solutions. We similarly offer an interpretation to determine the stable and unstable solutions based on the resource of a computational machine, such that the solutions are (un) stable if computational resource (decreases) increases with the increase of temperature. We observe that the effect of anisotropy on holographic subregion complexity is decreasing. This decreasing effect can be interpreted by considering a whole closed system consisting of the state and its environment in which the complexity of the mixed state decreases and complexity of the environment increases.

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Complexity growth in flat spacetimes

Cited by 17 publications

References 67 publications

Black hole subregion action and complexity

Black hole subregion action and complexity

Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity

Note on stability and holographic subregion complexity

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