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Does Complexity Equal Anything?
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Does Complexity Equal Anything?
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We present a new infinite class of gravitational observables in asymptotically Anti-de Sitter space living on codimension-one slices of the geometry, the most famous of which is the volume of the maximal slice. We show that these observables display universal features for the thermofield-double state: they grow linearly in time at late times and reproduce the switch-back effect in shock wave geometries. We argue that any member of this class of observables is an equally viable candidate as the extremal volume for a gravitational dual of complexity.
Forward citations
Cited by 22 Pith papers
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Comments on holographic spread complexity
The momentum–spread-complexity relation requires generalized coherent states adapted to the spacetime symmetry algebra; semiclassical spreading alone cannot produce a momentum–complexity correspondence.
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Complexity Inequalities for Quantum Subsystems
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for comp...
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Complexity Inequalities for Quantum Subsystems
Introduces tripartite complexity and complexity gap for three-region subsystems and reports that the gap has a definite sign in holographic volume complexity, Fisher-Rao Gaussian complexity, and Krylov-space approaches.
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Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity
Exact Krylov correlators in sl(2,R) models are proportional to proper radial momenta of infalling particles in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
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Universal Time Evolution of Holographic and Quantum Complexity
Holographic complexity measures show universal linear growth followed by late-time saturation, proven necessary and sufficient via pole structures in the energy basis using the residue theorem, arising from random mat...
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Holographic timelike complexity for de Sitter
Timelike subregion volume complexity in de Sitter grows exponentially early and diverges hyperfast at a maximal duration; near the SdS black hole horizon the divergence is replaced by slower, claimed-nonlinear growth.
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Page transition for the complexity of an evaporating black hole
The complexity of radiation from an evaporating black hole is argued to undergo a sharp Page-like transition, dominated after the Page time by the volume of an island in the entanglement wedge.
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Non-perturbative saturation of Krylov complexity, and its implications in quantum gravity
Full-spectrum Krylov complexity provably saturates at ~e^{S(E)} log(1/λ) in every low-energy state — near the energy-dependent Heisenberg time, not the maximal e^{S_max} — because discrete-spectrum orthogonal polynomi...
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Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity
Exact Krylov correlators in sl(2,R) models are proportional to radial momenta in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
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Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity
Exact Krylov correlators in sl(2,R) models are proportional to radial momenta of infalling particles in the BTZ black hole, providing a step toward generalizing the complexity-momentum correspondence.
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Bridging Krylov Complexity and Universal Analog Quantum Simulator
Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.
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Probing holographic conformal field theories
In a holographic CFT on a cylinder, a qutrit Unruh-DeWitt detector harvests more mana when the dual bulk scalar uses standard (Δ+) quantization than alternate (Δ−) quantization.
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Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specif...
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Toward Krylov-based holography in double-scaled SYK
Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-ge...
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Holography of K-complexity: Switchbacks and Shockwaves
Operator Krylov complexity in triple-scaled DSSYK matches JT-gravity geodesic lengths with shockwaves and exhibits the switchback effect when the Lanczos algorithm is perturbed by two-sided operator insertions.
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$T\bar{T}$ deformation and multiple-flavor Lorentzian threads
TTbar-induced corrections to complexity=anything expand into generalized Willmore functionals that admit a local multi-flavor Lorentzian-thread decomposition by curvature sector.
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Holographic complexity of de-Sitter black holes
In SdS black hole holography, CV and CV2.0 complexities grow linearly while CA growth vanishes due to finite action, with matching rates between static patch and dS/CFT schemes.
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Holographic complexity of conformal fields in global de Sitter spacetime
Holographic complexity of CFTs in global dS_d is computed via volume and action prescriptions in AdS foliation and brane setups, then compared to results from static and Poincare patches.
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Stringy Effects on Holographic Complexity: The Complete Volume in Dynamical Spacetimes
Gauss-Bonnet corrections to the complete volume proposal introduce a competition effect in static black holes while preserving momentum-governed growth rates and logarithmic scrambling times in dynamical Vaidya geometries.
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Stringy Effects on Holographic Complexity: The Complete Volume in Dynamical Spacetimes
Gauss-Bonnet corrections to the complete volume introduce a competition effect in static cases and prolong the critical time in two-sided shocks while the complexity growth rate stays governed by conserved momentum.
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Probing holographic conformal field theories
A boundary-coupled qutrit detector harvests more mana for the standard (Δ+) than the alternate (Δ−) scalar quantization in global AdS_4/CFT_3, in principle reading off the bulk boundary condition.
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Holographic complexity of the Klebanov-Strassler background
Studies holographic complexity in the Klebanov-Strassler background, reporting common scaling with confinement scale across functionals and more complex UV divergences than in AdS.
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