Simulating Holographic Conformal Field Theories on Hyperbolic Lattices

Area of Science:

• Theoretical Physics
• Quantum Gravity
• Condensed Matter Physics

Background:

• The bulk-boundary correspondence links gravitational theories in anti-de-Sitter (AdS) space to conformal field theories (CFTs) on its boundary.
• Simulating this correspondence often requires complex theoretical frameworks or large-scale experiments.

Purpose of the Study:

• To develop a tabletop experimental model that universally encodes aspects of the AdS/CFT correspondence.
• To simulate gravitational self-interactions and emergent CFTs in a controlled setting.
• To propose and validate an experimentally feasible method for measuring holographic CFT data.

Main Methods:

• Utilizing hyperbolic lattices combined with nonlinear dynamics.
• Constructing a holographic toy model that simulates bulk gravitational self-interactions.
• Measuring CFT data through two- and three-point functions.
• Simulating a thermal CFT via an effective black hole geometry.
• Proposing and simulating an electrical circuit protocol for experimental measurement.

Main Results:

• The tabletop setting successfully encodes key aspects of the bulk-boundary correspondence.
• The model exhibits an emergent CFT with non-trivial boundary correlations.
• The study clarifies the simulation of a thermal CFT through an effective black hole geometry.
• An experimentally feasible protocol for measuring holographic CFT using electrical circuits was proposed and simulated.

Conclusions:

• Tabletop experiments with hyperbolic lattices and nonlinear dynamics offer a universal platform for studying the AdS/CFT correspondence.
• The developed holographic toy model provides a concrete and broadly applicable tool for simulating quantum gravity phenomena.
• Electrical circuits present a viable experimental avenue for measuring holographic CFT data, bridging theoretical concepts with practical observation.