Pedraza, Juan F;
Russo, Andrea;
Svesko, Andrew;
Weller-Davies, Zachary;
(2021)
Lorentzian Threads as Gatelines and Holographic Complexity.
Physical Review Letters
, 127
(27)
, Article 271602. 10.1103/PhysRevLett.127.271602.
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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 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."
| Type: | Article |
|---|---|
| Title: | Lorentzian Threads as Gatelines and Holographic Complexity |
| Location: | United States |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1103/PhysRevLett.127.271602 |
| Publisher version: | https://doi.org/10.1103/PhysRevLett.127.271602 |
| Language: | English |
| Additional information: | Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10143114 |
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