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Complexity Equals Anything II
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Complexity Equals Anything II
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We expand on our results in arXiv:2111.02429 to present a broad new class of gravitational observables in asymptotically Anti-de Sitter space living on general codimension-zero regions of the bulk spacetime. By taking distinct limits, these observables can reduce to well-studied holographic complexity proposals, e.g., the volume of the maximal slice and the action or spacetime volume of the Wheeler-DeWitt patch. As with the codimension-one family found in arXiv:2111.02429, these new observables display two key universal features for the thermofield double state: they grow linearly in time at late times and reproduce the switchback effect. Hence we argue that any member of this new class of observables is an equally viable candidate as a gravitational dual of complexity. Moreover, using the Peierls construction, we show that variations of the codimension-zero and codimension-one observables are encoded in the gravitational symplectic form on the semi-classical phase-space, which can then be mapped to the CFT.
Forward citations
Cited by 12 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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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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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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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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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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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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A Timelike Quantum Focusing Conjecture
A timelike quantum focusing conjecture implies a complexity-based quantum strong energy condition and a complexity bound analogous to the covariant entropy bound for suitable codimension-0 field theory complexity measures.
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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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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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