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Holographic de Sitter Geometry from Entanglement in Conformal Field Theory
Jan de Boer1, Michal P Heller2, Robert C Myers2
1Institute for Theoretical Physics, University of Amsterdam, 1090 GL Amsterdam, Netherlands.
Physical Review Letters
|February 27, 2016
Summary
Small perturbations in conformal field theories (CFTs) exhibit holographic entanglement organization. Entanglement entropy changes follow a Klein-Gordon equation in de Sitter spacetime, with sphere size acting as emergent time.
Area of Science:
- Quantum Field Theory
- String Theory and Holography
- Condensed Matter Physics
Background:
- Conformal field theories (CFTs) are crucial for understanding critical phenomena in diverse physical systems.
- Entanglement entropy quantifies quantum correlations and is a key observable in CFTs.
- Holographic principles suggest a connection between gravitational theories and quantum field theories.
Purpose of the Study:
- To investigate the structure of entanglement for small perturbations around the vacuum in general CFTs.
- To explore a novel holographic organization of entanglement entropy.
- To analyze the behavior of entanglement entropy for spherical regions in CFTs.
Main Methods:
- Analyzing small perturbations of the vacuum state in general CFTs.
- Considering spherical entangling regions within a constant time slice.
- Deriving and solving the Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime.
Main Results:
- Demonstrated a novel holographic organization of entanglement for small perturbations in general CFTs.
- Showed that perturbations in entanglement entropy for spherical regions satisfy a Klein-Gordon equation in dS spacetime.
- Identified the size of the entangling sphere as the emergent timelike direction in dS spacetime.
Conclusions:
- Entanglement structure in perturbed CFTs is governed by holographic principles.
- The dynamics of entanglement entropy perturbations can be mapped to scalar fields in dS spacetime.
- Additional conserved charges in CFTs lead to multiple dynamical scalar fields in the holographic dual.
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