Simulating Holographic Conformal Field Theories on Hyperbolic Lattices

Simulating Holographic Conformal Field Theories on Hyperbolic Lattices

13 Aug 2024 | Santanu Dey, Anfanny Chen, Pablo Basteiro, Alexander Fritzche, Martin Greiter, Matthias Kaminski, Patrick M. Lenggenhager, René Meyer, Riccardo Sorbello, Alexander Stegmaier, Ronny Thomale, Johanna Erdmenger, Igor Boettcher
This paper presents a method to simulate holographic conformal field theories (CFTs) on hyperbolic lattices, demonstrating how table-top experiments can encode aspects of the bulk-boundary correspondence between gravity in anti-de Sitter (AdS) space and CFTs. The proposed holographic toy model simulates gravitational self-interactions in the bulk and features an emergent CFT with nontrivial correlations on the boundary. The model measures CFT data from two- and three-point functions and clarifies how a thermal CFT is simulated through an effective black hole geometry. A concrete example is the simulation of an experimentally feasible protocol to measure the holographic CFT using electrical circuits. The holographic principle, as realized by the AdS/CFT correspondence, posits a deep connection between scale-invariant theories near second-order phase transitions (CFTs) and quantum gravity in curved spacetimes. The correspondence states that gravity in a negatively curved space is dual to a CFT on its boundary. The presence of a black hole in the bulk results in a thermal CFT, with the temperature given by the Hawking temperature. While numerous calculations support the correspondence, experimental verification is challenging due to the need to observe or simulate graviton-graviton interactions. The goal of this work is to construct a concrete holographic toy model for the AdS/CFT correspondence that can be realized in the laboratory. The model uses four key ingredients: (i) a lattice realization of AdS space through hyperbolic lattices, (ii) nonlinear dynamical equations to emulate gravitational self-interactions, (iii) effective black hole geometries to emulate temperature, and (iv) a theoretical framework and experimental protocol to compute and measure boundary correlation functions. The model demonstrates that even classical platforms can be holographic, corresponding to the limit where weakly-coupled semiclassical bulk gravity is dual to a strongly coupled CFT. The paper extends previous works on holographic aspects of hyperbolic lattices by systematically studying higher-point correlation functions and their CFT data, precisely characterizing thermal correlations, and providing a theoretical framework and experimental protocol to measure boundary correlations. It also simulates an experimental setup satisfying the four ingredients, demonstrating that the CFT data for both type-I and type-II lattices is identical, indicating they are the same CFTs at zero and finite temperatures. The results solidify the interpretation of type-II lattices as geometries that emulate black holes.This paper presents a method to simulate holographic conformal field theories (CFTs) on hyperbolic lattices, demonstrating how table-top experiments can encode aspects of the bulk-boundary correspondence between gravity in anti-de Sitter (AdS) space and CFTs. The proposed holographic toy model simulates gravitational self-interactions in the bulk and features an emergent CFT with nontrivial correlations on the boundary. The model measures CFT data from two- and three-point functions and clarifies how a thermal CFT is simulated through an effective black hole geometry. A concrete example is the simulation of an experimentally feasible protocol to measure the holographic CFT using electrical circuits. The holographic principle, as realized by the AdS/CFT correspondence, posits a deep connection between scale-invariant theories near second-order phase transitions (CFTs) and quantum gravity in curved spacetimes. The correspondence states that gravity in a negatively curved space is dual to a CFT on its boundary. The presence of a black hole in the bulk results in a thermal CFT, with the temperature given by the Hawking temperature. While numerous calculations support the correspondence, experimental verification is challenging due to the need to observe or simulate graviton-graviton interactions. The goal of this work is to construct a concrete holographic toy model for the AdS/CFT correspondence that can be realized in the laboratory. The model uses four key ingredients: (i) a lattice realization of AdS space through hyperbolic lattices, (ii) nonlinear dynamical equations to emulate gravitational self-interactions, (iii) effective black hole geometries to emulate temperature, and (iv) a theoretical framework and experimental protocol to compute and measure boundary correlation functions. The model demonstrates that even classical platforms can be holographic, corresponding to the limit where weakly-coupled semiclassical bulk gravity is dual to a strongly coupled CFT. The paper extends previous works on holographic aspects of hyperbolic lattices by systematically studying higher-point correlation functions and their CFT data, precisely characterizing thermal correlations, and providing a theoretical framework and experimental protocol to measure boundary correlations. It also simulates an experimental setup satisfying the four ingredients, demonstrating that the CFT data for both type-I and type-II lattices is identical, indicating they are the same CFTs at zero and finite temperatures. The results solidify the interpretation of type-II lattices as geometries that emulate black holes.
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