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Journal of High Energy Physics

, 2018:44 | Cite as

Holographic complexity and volume

  • Josiah Couch
  • Stefan Eccles
  • Ted JacobsonEmail author
  • Phuc Nguyen
Open Access
Regular Article - Theoretical Physics

Abstract

The previously proposed “Complexity=Volume” or CV-duality is probed and developed in several directions. We show that the apparent lack of universality for large and small black holes is removed if the volume is measured in units of the maximal time from the horizon to the “final slice” (times Planck area). This also works for spinning black holes. We make use of the conserved “volume current”, associated with a foliation of spacetime by maximal volume slices, whose flux measures their volume. This flux picture suggests that there is a transfer of the complexity from the UV to the IR in holographic CFTs, which is reminiscent of thermalization behavior deduced using holography. It also naturally gives a second law for the complexity when applied at a black hole horizon. We further establish a result supporting the conjecture that a boundary foliation determines a bulk maximal foliation without gaps, establish a global inequality on maximal volumes that can be used to deduce the monotonicity of the complexification rate on a boost-invariant background, and probe CV duality in the settings of multiple quenches, spinning black holes, and Rindler-AdS.

Keywords

AdS-CFT Correspondence Black Holes 

Notes

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.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Josiah Couch
    • 1
  • Stefan Eccles
    • 1
  • Ted Jacobson
    • 2
    Email author
  • Phuc Nguyen
    • 2
  1. 1.Theory Group, Department of PhysicsThe University of Texas at AustinAustinU.S.A.
  2. 2.Maryland Center for Fundamental Physics and Department of PhysicsUniversity of MarylandCollege ParkU.S.A.

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