REVIEW 4 cited by
Lorentzian threads as 'gatelines' and holographic complexity
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Lorentzian threads as 'gatelines' and holographic complexity
read the original abstract
The continuous min flow-max cut principle is used to reformulate the 'complexity=volume' conjecture using Lorentzian flows -- divergenceless norm-bounded timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. The nesting property is used to show the rate of complexity is bounded below by "conditional complexity", describing a multi-step optimization with intermediate and final target states. Conceptually, discretized Lorentzian flows are interpreted in terms of threads or gatelines such that complexity is equal to the minimum number of gatelines used to prepare a CFT state by an optimal tensor network (TN) discretizing the state. We propose a refined measure of complexity, capturing the role of suboptimal TNs, as an ensemble average. The bulk symplectic potential provides a 'canonical' thread configuration characterizing perturbations around arbitrary CFT states. Its consistency requires the bulk to obey linearized Einstein's equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating a notion of 'spacetime complexity'.
Forward citations
Cited by 4 Pith papers
-
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.
-
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...
-
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...
-
$T\bar{T}$ 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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.