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Pseudoentropy in dS/CFT and Timelike Entanglement Entropy
Kazuki Doi1, Jonathan Harper1, Ali Mollabashi1
1Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan.
Physical Review Letters
|February 10, 2023
Summary
Holographic entanglement entropy in dS/CFT and timelike entanglement entropy in CFTs are complex pseudoentropies. Their imaginary parts reveal the emergence of time in dS/CFT, offering new insights into quantum gravity and spacetime.
Area of Science:
- Theoretical Physics
- Quantum Gravity
- String Theory
Background:
- Entanglement entropy quantifies quantum correlations in a system.
- Holographic entanglement entropy (HEE) relates boundary theory entropy to bulk geometry in AdS/CFT.
- dS/CFT correspondence extends holographic principles to de Sitter spacetime.
Purpose of the Study:
- To introduce and study timelike entanglement entropy in Conformal Field Theories (CFTs).
- To investigate the nature of holographic entanglement entropy in dS/CFT.
- To establish a connection between these two concepts and their implications for spacetime.
Main Methods:
- Introducing timelike entanglement entropy for CFTs.
- Calculating holographic entanglement entropy in dS/CFT.
- Utilizing analytical continuation to relate different entanglement measures.
- Interpreting the results within the framework of pseudoentropy.
Main Results:
- Both holographic entanglement entropy in dS/CFT and timelike entanglement entropy in CFTs generally yield complex values.
- These complex values are related through analytical continuation.
- The study argues for understanding these measures as pseudoentropy.
- The imaginary part of pseudoentropy is shown to imply the emergence of time in dS/CFT.
Conclusions:
- Timelike entanglement entropy and holographic entanglement entropy in dS/CFT are unified under the concept of pseudoentropy.
- The imaginary component of pseudoentropy provides a novel mechanism for the emergence of time in de Sitter spacetime.
- This work offers a new perspective on the interplay between quantum information and spacetime geometry in holographic contexts.
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