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Holographic Complexity Equals Bulk Action?

Adam R Brown1, Daniel A Roberts2, Leonard Susskind1

  • 1Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, California 94305, USA.

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|May 28, 2016
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Summary
This summary is machine-generated.

We propose that quantum complexity in holographic states is linked to the action of a specific spacetime region, the Wheeler-DeWitt patch. This new conjecture improves upon earlier ideas and suggests black holes may be nature's fastest computers.

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Area of Science:

  • Quantum gravity
  • Holographic principle
  • Black hole physics

Background:

  • Previous conjecture linked quantum complexity to spatial volume.
  • Need for a more accurate measure of holographic complexity.

Purpose of the Study:

  • To propose and test a new conjecture for quantum complexity in holographic states.
  • To explore the relationship between quantum complexity and spacetime geometry.

Main Methods:

  • Conjecturing quantum complexity is dual to the action of a Wheeler-DeWitt patch.
  • Testing the conjecture using various black hole models in anti-de Sitter spacetime.
  • Analyzing black holes perturbed by shells and shock waves.

Main Results:

  • The Wheeler-DeWitt patch action provides a better measure of quantum complexity than spatial volume.
  • The conjecture holds for neutral, charged, and rotating black holes.
  • The study provides evidence for the conjecture in perturbed black hole systems.

Conclusions:

  • The Wheeler-DeWitt patch conjecture offers a significant advancement in understanding holographic quantum complexity.
  • The findings support the hypothesis that black holes operate as the fastest possible computers.