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Null Wave Front and Ryu-Takayanagi Surface.

Jun Tsujimura1, Yasusada Nambu1

  • 1Department of Physics, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602, Japan.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

The Ryu-Takayanagi formula connects quantum entanglement entropy to minimal surfaces in gravity. This study proposes a causal holographic information flow, showing wave fronts of null geodesics can represent these minimal surfaces.

Keywords:
Ryu–Takayanagi surfaceextremal surfacenull geodesicswave frontwave optics

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Area of Science:

  • Theoretical Physics
  • Quantum Information Theory
  • Holography

Background:

  • The Ryu-Takayanagi formula relates entanglement entropy in quantum field theory to the area of minimal surfaces in a dual gravitational theory.
  • Existing research explores interpreting this formula as a flow rather than a static surface.

Purpose of the Study:

  • To investigate the interpretation of the Ryu-Takayanagi formula as a flow.
  • To construct a flow representing causal holographic information using null rays from the AdS boundary.
  • To establish conditions under which this causal information flow corresponds to the Ryu-Takayanagi surface.

Main Methods:

  • Consideration of null rays emitted from the Anti-de Sitter (AdS) boundary.
  • Construction of a flow representing causal holographic information.
  • Analysis of spherical symmetric static spacetimes with a negative cosmological constant.
  • Identification of wave fronts of null geodesics as extremal surfaces.

Main Results:

  • A sufficient and necessary condition is presented for the causal information surface to coincide with the Ryu-Takayanagi surface.
  • In specific spacetimes, wave fronts of null geodesics from an AdS boundary point are shown to be extremal surfaces.
  • These wave fronts can thus be identified as Ryu-Takayanagi surfaces.

Conclusions:

  • The study provides a flow-based interpretation of holographic entanglement entropy.
  • It demonstrates that causal information surfaces, represented by wave fronts of null geodesics, can be equivalent to Ryu-Takayanagi surfaces under certain conditions.
  • A novel wave optical formula for calculating causal holographic information is proposed.