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arxiv: 2305.04862 · v3 · submitted 2023-05-05 · ✦ hep-lat · gr-qc

Testing holographic duality in hyperbolic lattices

Jingming Chen , Feiyu Chen , Linyun Yang , Yuting Yang , Liren Chen , Zihan Chen , Ying Wu , Yan Meng
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Bei Yan Xiang Xi Zhenxiao Zhu Minqi Cheng Gui-Geng Liu Perry Ping Shum Hongsheng Chen Rong-Gen Cai Run-Qiu Yang Yihao Yang Zhen Gao
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Pith reviewed 2026-05-24 08:22 UTC · model grok-4.3

classification ✦ hep-lat gr-qc
keywords holographic dualityhyperbolic latticesboundary CFTRyu-Takayanagi formulascalar field propagatorentanglement entropyAdS/CFT
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The pith

Hyperbolic lattice circuits reproduce the boundary CFT two-point function and Ryu-Takayanagi entanglement entropy from a measured bulk scalar propagator.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to test the holographic duality conjecture by constructing physical circuits on hyperbolic lattices that approximate three-dimensional anti-de Sitter space. Researchers measure the propagator of a classical scalar field across this discrete geometry and show that the resulting equal-time correlations on the boundary match the functional form expected for a two-dimensional conformal field theory, including the correct exponential decay with separation and the relation between field mass and conformal dimension. They then extract the entanglement entropy of a boundary interval directly from those correlations and verify that it equals the length of the minimal bulk curve connecting the interval endpoints, as required by the Ryu-Takayanagi formula. A sympathetic reader would care because the experiment supplies the first concrete laboratory realization in which quantum boundary data are recovered from classical bulk propagation, offering a route to study strongly coupled systems without solving the quantum theory directly.

Core claim

By experimentally measuring the classical scalar field propagator in hyperbolic circuits, the equal-time two-point correlation function of the dual boundary conformal field theory is reproduced, verifying its exponential dependence on the boundary separation and the conformal dimension-scalar mass relation. Furthermore, by leveraging the two-point correlation function, the entanglement entropy for a boundary CFT subsystem is reconstructed, confirming that it follows the Ryu-Takayanagi formula.

What carries the argument

Hyperbolic lattice circuits that discretize anti-de Sitter geometry, in which the measured scalar-field propagator on the lattice directly supplies the boundary two-point function of the dual CFT.

Load-bearing premise

The propagator measured on the discrete hyperbolic circuit accurately stands in for the continuum bulk scalar field whose boundary values are dictated by the holographic dictionary.

What would settle it

A measured boundary correlation function that fails to decay exponentially with separation or that violates the expected mass-to-conformal-dimension mapping would falsify the claimed reproduction of the duality.

read the original abstract

The celebrated holographic duality posits a correspondence between a quantum gravity in a bulk spacetime and a quantum field theory (QFT) defined on its lower-dimensional boundary. This duality not only offers deep insights into the enigmatic nature of quantum gravity but also provides an efficient methodology for studying strongly correlated systems. However, despite its profound significance in modern physics, holographic duality remains a conjecture, and further experimental exploration is highly sought after. Here, we present the first experimental test of holographic duality between a three-dimensional bulk gravity and a two-dimensional boundary QFT using hyperbolic lattices. By experimentally measuring the classical scalar field propagator in hyperbolic circuits, we reproduce the equal-time two-point correlation function of the dual boundary conformal field theory (CFT), verifying its exponential dependence on the boundary separation and the conformal dimension-scalar mass relation. Furthermore, by leveraging the two-point correlation function, we reconstruct the entanglement entropy for a boundary CFT subsystem, confirming that it follows the Ryu-Takayanagi formula. These results constitute the first direct experimental evidence that quantum properties of the QFT can be holographically reproduced through its dual classical field in curved space. This heuristic experimental effort opens a new avenue for in-depth investigations on the holographic duality and extensive exploration of quantum-gravity-inspired phenomena in classical systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims to present the first experimental test of holographic duality between 3D bulk gravity and 2D boundary QFT using hyperbolic lattices. By measuring the classical scalar field propagator in hyperbolic circuits, the authors reproduce the equal-time two-point correlation function of the dual boundary CFT (including its exponential dependence on boundary separation and the conformal dimension-scalar mass relation) and reconstruct the entanglement entropy of a boundary subsystem, confirming agreement with the Ryu-Takayanagi formula. This is presented as direct experimental evidence that quantum properties of the QFT can be holographically reproduced via its dual classical field in curved space.

Significance. If the discrete-circuit results survive continuum extrapolation and independent verification against the exact AdS Green function, the work would constitute a notable experimental step toward testing the holographic dictionary in a controlled classical setting, with potential to inspire further quantum-gravity-inspired circuit experiments. The absence of such controls in the reported analysis, however, limits the current strength of the claim.

major comments (2)
  1. [Abstract] Abstract: The central claim that the measured propagator reproduces the holographic two-point function and verifies the conformal-dimension–mass relation assumes the finite discrete hyperbolic circuit faithfully approximates the continuum bulk-to-boundary propagator of AdS. No continuum extrapolation, no direct comparison to the exact continuum AdS Green function at the same mass, and no quantification of how boundary correlators change under lattice refinement are reported; any observed match could therefore arise from lattice-scale corrections rather than the duality itself.
  2. [Abstract] Abstract: The reconstruction of entanglement entropy via the two-point function and its agreement with the Ryu-Takayanagi formula is presented without reported error bars, exclusion criteria, or circuit-size dependence. This information is load-bearing for assessing whether the reported match is robust or sensitive to finite-size effects and analysis choices.
minor comments (1)
  1. [Abstract] Abstract: The abstract would be clearer if it stated the range of circuit sizes or boundary separations over which the exponential decay was observed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed reading and the constructive critique of our claims. We address each major comment below. Where the manuscript is missing explicit controls, we will revise to strengthen the presentation; where the discrete nature of the experiment is inherent to the setup, we explain the rationale without overstating the continuum limit.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the measured propagator reproduces the holographic two-point function and verifies the conformal-dimension–mass relation assumes the finite discrete hyperbolic circuit faithfully approximates the continuum bulk-to-boundary propagator of AdS. No continuum extrapolation, no direct comparison to the exact continuum AdS Green function at the same mass, and no quantification of how boundary correlators change under lattice refinement are reported; any observed match could therefore arise from lattice-scale corrections rather than the duality itself.

    Authors: We agree that an explicit continuum extrapolation and a side-by-side comparison with the exact AdS Green function would strengthen the claim. The hyperbolic circuit is a fixed discrete realization chosen to embed the hyperbolic geometry; the measured propagator exhibits the expected exponential decay with boundary separation and the mass–dimension relation over the accessible range. In the revised manuscript we will add (i) a direct numerical comparison of the lattice propagator to the continuum AdS bulk-to-boundary Green function at the same scalar mass and (ii) a brief discussion of how the two-point function changes when the circuit is refined within the experimentally accessible sizes. These additions will make clear the extent to which the observed match is protected by the lattice construction versus possible finite-spacing artifacts. revision: yes

  2. Referee: [Abstract] Abstract: The reconstruction of entanglement entropy via the two-point function and its agreement with the Ryu-Takayanagi formula is presented without reported error bars, exclusion criteria, or circuit-size dependence. This information is load-bearing for assessing whether the reported match is robust or sensitive to finite-size effects and analysis choices.

    Authors: We accept that the absence of error bars and circuit-size dependence weakens the robustness assessment. The entanglement entropy is obtained by integrating the measured two-point function over the subsystem; the experimental data carry statistical uncertainties from the circuit measurements. In the revision we will (i) report error bars propagated from the raw propagator data, (ii) state the exclusion criteria used for outlier runs, and (iii) show the reconstructed entropy for the two largest available circuit sizes to illustrate finite-size stability. These changes will allow readers to judge the sensitivity of the Ryu-Takayanagi agreement to analysis choices. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental verification relies on independent measurements

full rationale

The paper reports an experimental measurement of the classical scalar propagator on a discrete hyperbolic circuit and compares it to the expected boundary two-point function and RT entanglement entropy from holographic duality. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or self-definitional ansatz; the central claim is an empirical match between circuit data and continuum holographic formulas, which remains falsifiable by the measurements themselves. The abstract and context contain no equations or procedures that rename a fit as a prediction or import uniqueness via prior self-citation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only text supplies no explicit free parameters, additional axioms, or invented entities beyond the holographic duality itself.

axioms (1)
  • domain assumption Holographic duality maps the bulk classical scalar field to the boundary CFT two-point function and entanglement entropy via the Ryu-Takayanagi prescription.
    The entire experimental claim rests on this correspondence holding for the chosen observables.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Tunable cornerlike states in topological type-II hyperbolic lattices

    cond-mat.mes-hall 2026-01 unverdicted novelty 7.0

    Type-II hyperbolic lattices host higher-order topological phases with zero-energy cornerlike states localized on both inner and outer boundaries, verified in modified BHZ and BBH models and robust to weak disorder.

Reference graph

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    Inset shows the same quasi-ideal type-I hyperbolic circuit in Extended Data Fig. 5a. b, Simulated conformal dimension ∆ (pink dots) verse mass-squared 𝑚𝑒𝑓𝑓 2, the green line is a theoretical fitting of equation (1) with effective boundary dimension 𝑑𝑏𝑒𝑓𝑓 = 1.028 and effective AdS radius -squared ℓ2 𝑒𝑓𝑓 = 0.836 . Inset displays the linear relation between ...

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