Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Correspondence

Area of Science:

• Theoretical Physics
• Quantum Gravity
• String Theory

Background:

• The surface-state correspondence is a theoretical framework linking boundary phenomena to bulk properties in certain quantum gravity theories.
• Understanding this correspondence is crucial for testing holographic principles and quantum gravity models.

Purpose of the Study:

• To demonstrate the validity of the surface-state correspondence within the Anti-de Sitter space/conformal field theory (AdS(3)/CFT(2)) framework.
• To generalize existing theoretical tools for analyzing this correspondence.

Main Methods:

• Generalization of the continuous multiscale entanglement renormalization group (MERA) ansatz.
• Incorporation of boundary states from conformal field theories (CFTs).
• Natural inclusion of bulk diffeomorphism symmetries.

Main Results:

• Identification of bulk local operators that accurately reproduce scalar field solutions and propagators in AdS(3).
• Calculation of the information metric for a locally excited state.
• Demonstration that the information metric reproduces the time slice of AdS(3).

Conclusions:

• The study provides a concrete realization of the surface-state correspondence in AdS(3)/CFT(2).
• The generalized MERA formulation effectively bridges bulk and boundary descriptions.
• The results offer new insights into the holographic principle and quantum information in curved spacetimes.