TY  - JOUR
IS  - 2
N2  - Holographic entanglement entropy was recently recast in terms of Riemannian flows or ?bit threads?. We consider the Lorentzian analog to reformulate the ?complexity=volume? conjecture using Lorentzian flows ? timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. By the nesting of Lorentzian flows, holographic complexity is shown to obey a number of properties. Particularly, the rate of complexity is bounded below by conditional complexity, describing a multi-step optimization with intermediate and final target states. We provide multiple explicit geometric realizations of Lorentzian flows in AdS backgrounds, including their time-dependence and behavior near the singularity in a black hole interior. Conceptually, discretized flows are interpreted as Lorentzian threads or ?gatelines?. Upon selecting a reference state, complexity thence counts the minimum number of gatelines needed to prepare a target state described by a tensor network discretizing the maximal volume slice, matching its quantum information theoretic definition. We point out that suboptimal tensor networks are important to fully characterize the state, leading us to propose a refined notion of complexity as an ensemble average. The bulk symplectic potential provides a specific ?canonical? thread configuration characterizing perturbations around arbitrary CFT states. Consistency of this solution requires the bulk satisfy the linearized Einstein?s equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating for a principle of ?spacetime complexity?. Lastly, we argue Lorentzian threads provide a notion of emergent time. This article is an expanded and detailed version of [1], including several new results.
UR  - https://doi.org/10.1007/JHEP02(2022)093
EP  - 123
ID  - discovery10151913
Y1  - 2022/02/11/
TI  - Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
AV  - public
PB  - SPRINGER
JF  - Journal of High Energy Physics
A1  - Pedraza, Juan F
A1  - Russo, Andrea
A1  - Svesko, Andrew
A1  - Weller-Davies, Zachary
KW  - Science & Technology
KW  -  Physical Sciences
KW  -  Physics
KW  -  Particles & Fields
KW  -  Physics
KW  -  AdS-CFT Correspondence
KW  -  Gauge-Gravity Correspondence
KW  -  BLACK-HOLE
KW  -  GEOMETRY
KW  -  ENTANGLEMENT
VL  - 2022
N1  - Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
ER  -