2021/05/31 by Juan F. Pedraza, Andrea Russo, Andrew Svesko +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Bounded function #Conformal map #Conservation law #Discretization #Measure (data warehouse) #Noncommutative and Quantum Gravity Theories #Quantum many-body systems #Symplectic geometry #Tensor (intrinsic definition) #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevlett.127.271602
published as Phys. Rev. Lett. 127, 271602 (2021) · 5 pages + Supplemental Material. v3: version accepted for publication in PRL
openalex created_date 2021/06/07 · arxiv created 2021/11/15 · openalex publication_date 2021/12/30 · arxiv updated 2022/01/04 · openalex updated_date 2026/08/05
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 multistep 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 conformal field theory (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."