Simulating Holographic Conformal Field Theories on Hyperbolic Lattices

Santanu Dey, Anffany Chen, Pablo Basteiro, Alexander Fritzsche, Martin Greiter, Matthias Kaminski, Patrick M. Lenggenhager, Rene Meyer, Riccardo Sorbello, Alexander Stegmaier, Ronny Thomale, Johanna Erdmenger, Igor Boettcher

Published 2024-04-03Version 1

We demonstrate how table-top settings combining hyperbolic lattices with nonlinear dynamics universally lead to a genuine realization of the bulk-boundary-correspondence between gravity in anti-de-Sitter (AdS) space and conformal field theory (CFT). Our concrete and broadly applicable holographic toy model simulates gravitational self-interactions in the bulk and features an emergent CFT with nontrivial correlations on the boundary. We measure the CFT data contained in the two- and three-point functions and clarify how a thermal CFT is simulated through an effective black hole geometry. As a concrete example, we propose and simulate an experimentally feasible protocol to measure the holographic CFT using electrical circuits.