Does Complexity Equal Anything?

Belin, Alexandre; Myers, Robert C.; Ruan, Shan-Ming; Sárosi, Gábor; Speranza, Antony J.

doi:10.1103/physrevlett.128.081602

Cited by 68 publications

(81 citation statements)

References 24 publications

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“…Comparing with the AdS case with a similar conserved momentum P v [47], we note that the extra minus sign in our definition of conserved momentum (5.4) is compensated by the fact that the stretched horizon at r min is the lower limit of integration here. In contrast, the asymptotic boundary in AdS is the upper limit instead.…”

Section: Time Evolution Of CVmentioning

confidence: 81%

“…The CV conjecture (1.3) identifies holographic complexity as the volume of a codimensionone extremal surface, where as before we take the 'boundary' time slice Σ to be the surfaces t R = −t L = τ L on the stretched horizons (i.e., r = ρ L) in the two static patches. To analyze the time evolution of extremal surfaces in dS d+1 , we follow the analysis presented for the extremal surfaces in asymptotically AdS spacetimes, e.g., see [47,63,64]. The idea is that with an appropriate gauge-fixing condition, the profile of the extremal surfaces is determined by solving for the motion of a classical particle moving in an effective potential.…”

Section: Time Evolution Of Extremal Surfaces In Ds D+1mentioning

confidence: 99%

“…A point worth stressing is the crucial difference between the potentials of dS d+1 and those typically studied in AdS d+1 is the former does not contain any local maximum. In asymptotically AdS d+1 black holes, the local maximum plays a vital role in producing the linear growth of holographic complexity, e.g., [47,63,64]. For later use, we also note that the equation determining the time coordinate is given by…”

Section: Time Evolution Of Extremal Surfaces In Ds D+1mentioning

confidence: 99%

“…As before, we are considering the symmetric configuration with t R = τ L = −t L in the following. As noted in [47], we can consider the time evolution of the extremal surface for an infinitesimal interval as generating a perturbation of the initial 'trajectory'. Then working with the original 'action' (5.1), the standard analysis yields the conclusion that the time derivative of the holographic complexity is given by the momentum P u evaluated on the 'end points', i.e., dC V dτ = 8 N P u (τ ) .…”

Section: Time Evolution Of CVmentioning

confidence: 99%

“…Roughly speaking, holographic complexity measures the difficulty (i.e., the resources needed) to construct a particular target state in the boundary theory from an unentangled reference state using a set of fundamental simple gates. From the viewpoint of the bulk spacetime (i.e., asymptotically AdS spacetime), it appears that the holographic complexity may be associated with a broad family of codimension-one and -zero gravitational observables [47,48]. However, the most studied of these are: complexity=volume (CV) [49,50], complexity=action (CA) [51,52] and complexity=spacetime volume (CV2.0) [53].…”

Section: Introductionmentioning

confidence: 99%

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Holographic Complexity in dS$_{d+1}$

Jørstad,

Myers,

Ruan

2022

Preprint

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We study the CV, CA, and CV2.0 approaches to holographic complexity in (d + 1)-dimensional de Sitter spacetime. We find that holographic complexity and corresponding growth rate presents universal behaviour for all three approaches. In particular, the holographic complexity exhibits 'hyperfast' growth [1] and appears to diverge with a universal power law at a (finite) critical time. We introduce a cutoff surface to regulate this divergence, and the subsequent growth of the holographic complexity is linear in time.

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Section: Time Evolution Of CVmentioning

confidence: 81%

Section: Time Evolution Of Extremal Surfaces In Ds D+1mentioning

confidence: 99%

Section: Time Evolution Of Extremal Surfaces In Ds D+1mentioning

confidence: 99%

Section: Time Evolution Of CVmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Holographic Complexity in dS$_{d+1}$

Jørstad,

Myers,

Ruan

2022

Preprint

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Anisotropic flows into black holes

Cáceres

Shashi

2023

J. High Energ. Phys.

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We consider anisotropic black holes in the context of holographic renormalization group (RG) flows. We construct an a-function that is stationary at the boundary and the horizon and prove that it is also monotonic in both the exterior and the interior of the black hole. In spite of the reduced symmetry, we find that the “radial” null energy condition is sufficient to ensure the existence of this monotonic a-function. After constructing the a-function, we explore a holographic anisotropic p-wave superfluid state as a concrete example and numerical testing grounds. In doing so, we find that the a-function exhibits nontrivial oscillations in the trans-IR regime while preserving monotonicity. We find evidence that such oscillations appear to drive the trans-IR flow into nontrivial fixed points. We conclude by briefly discussing how our work fits into both the broader program of holographic RG flow and quantum information approaches to probing the black hole interior.

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Generalized volume-complexity for two-sided hyperscaling violating black branes

Omidi

2023

J. High Energ. Phys.

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In this paper, we investigate generalized volume-complexity $$ \mathcal{C} $$ C gen for a two-sided uncharged HV black brane in d + 2 dimensions. This quantity which was recently introduced in [48], is an extension of volume in the Complexity=Volume (CV) proposal, by adding higher curvature corrections with a coupling constant λ to the volume functional. We numerically calculate the growth rate of $$ \mathcal{C} $$ C gen for different values of the hyperscaling violation exponent θ and dynamical exponent z. It is observed that $$ \mathcal{C} $$ C gen always grows linearly at late times provided that we choose λ properly. Moreover, it approaches its late time value from below. For the case λ = 0, we find an analytic expression for the late time growth rate for arbitrary values of θ and z. However, for λ ≠ 0, the late time growth rate can only be calculated analytically for some specific values of θ and z. We also examine the dependence of the growth rate on d, θ, z and λ. Furthermore, we calculate the complexity of formation obtained from volume-complexity and show that it is not UV divergent. We also examine its dependence on the thermal entropy and temperature of the black brane. At the end, we also numerically calculate the growth rate of $$ \mathcal{C} $$ C gen for the case where the higher curvature corrections are a linear combination of the Ricci scalar, square of the Ricci tensor and square of the Riemann tensor. We show that for appropriate values of the coupling constants, the late time growth rate is again linear.

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Does Complexity Equal Anything?

Cited by 68 publications

References 24 publications

Holographic Complexity in dS$_{d+1}$

Holographic Complexity in dS$_{d+1}$

Anisotropic flows into black holes

Generalized volume-complexity for two-sided hyperscaling violating black branes

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