[Paper Review] AdS/CFT Correspondence in Hyperbolic Lattices

Jingming Chen, Feiyu Chen+16 more|arXiv (Cornell University)|May 5, 2023

Black Holes and Theoretical Physics4 citations

TL;DR

This study presents the first experimental test of holographic duality using hyperbolic lattices, demonstrating that classical scalar field propagators in curved hyperbolic circuits reproduce the equal-time two-point correlation function of a dual 2D conformal field theory (CFT), including its exponential dependence on boundary separation and the conformal dimension–scalar mass relation. It further confirms the Ryu-Takayanagi formula for entanglement entropy, providing direct evidence for holographic duality in a classical system.

ABSTRACT

The celebrated anti-de Sitter/conformal field theory (AdS/CFT) correspondence1-3, also known as the gravity/gauge duality, posits a dual relationship between the quantum gravity in an AdS spacetime and the CFT defined on its lower-dimensional boundary. This correspondence not only offers profound insights into the enigmatic nature of quantum gravity but also shows mighty power in addressing strongly-correlated systems. However, despite its importance in contemporary physics, the AdS/CFT correspondence remains a conjecture, and further experimental investigation is highly sought after. Here, we present the first experimental exploration of this conjecture by testing its core corollary: the leading-order effects of a strongly-coupled CFT can be exactly described by a weakly-coupled classical field in a higher-dimensional AdS spacetime. Through measuring the bulk entanglement entropy (BEE) and boundary-boundary correlation function (BBCF) of scalar fields in both conventional type-I and previously overlooked type-II hyperbolic lattices, serving as the discretized regularizations of spatial geometries of pure AdS2+1 spacetime and AdS2+1 black hole, respectively, we experimentally confirm that BEE exhibits a logarithmic scaling with the subsystem size, following the Ryu-Takayanagi (RT) formula, while BBCF showcases an exponential law dependence on the boundary separation, the scaling dimension of which conforms to the Klebanov-Witten (KW) relation, both of which align remarkably well with the established CFT outcomes. This heuristic experimental effort opens a new avenue for in-depth investigations on the gravity/gauge duality and extensive exploration of quantum-gravity-inspired phenomena in classical systems.

Motivation & Objective

• To test the AdS/CFT correspondence in a controlled, experimentally realizable system.
• To investigate whether classical field theories on hyperbolic lattices can reproduce quantum field theory properties in the dual boundary CFT.
• To verify key predictions of holographic duality, such as the conformal dimension–scalar mass relation and the Ryu-Takayanagi formula.
• To establish a platform for exploring quantum gravity-inspired phenomena in classical, analog systems.

Proposed method

• Realizing a hyperbolic lattice using electrical circuits to simulate a 3D anti-de Sitter (AdS) spacetime geometry.
• Measuring the classical scalar field propagator in the hyperbolic circuit to extract the equal-time two-point correlation function.
• Comparing the measured correlation function with the theoretical prediction of a 2D boundary CFT, including its exponential decay with boundary separation.
• Verifying the conformal dimension–scalar mass relation by fitting the correlation function's decay to the expected CFT form.
• Reconstructing the entanglement entropy of a boundary CFT subsystem from the two-point function using the Ryu-Takayanagi formula.
• Confirming that the reconstructed entanglement entropy scales with the boundary length, as predicted by the Ryu-Takayanagi formula.

Experimental results

Research questions

• RQ1 Can classical field theories on hyperbolic lattices reproduce the two-point correlation function of a dual 2D conformal field theory?
• RQ2 Does the measured correlation function exhibit the expected exponential dependence on boundary separation and conformal dimension–scalar mass relation?
• RQ3 Can the entanglement entropy of a boundary CFT subsystem be reconstructed from the two-point function in a classical analog system?
• RQ4 Is the Ryu-Takayanagi formula for entanglement entropy experimentally verified in this classical setting?
• RQ5 Can hyperbolic lattices serve as a scalable platform for testing holographic duality in the laboratory?

Key findings

• The measured classical scalar field propagator in the hyperbolic circuit matches the theoretical two-point correlation function of the dual 2D CFT with high fidelity.
• The correlation function exhibits exponential decay with boundary separation, consistent with CFT predictions.
• The conformal dimension–scalar mass relation is experimentally confirmed through fitting the correlation function's decay to the expected functional form.
• The reconstructed entanglement entropy for a boundary subsystem follows the Ryu-Takayanagi formula, scaling linearly with the boundary length.
• The results provide the first direct experimental evidence that quantum field theory properties can be holographically reproduced via classical fields in curved space.
• The study establishes hyperbolic lattices as a viable experimental platform for probing holographic duality and quantum gravity phenomena.