Breitenlohner-Freedman bound on hyperbolic tilings

Abstract

We establish how the Breitenlohner-Freedman (BF) bound is realized on tilings of two-dimensional Euclidean Anti-de Sitter space. For the continuum, the BF bound states that on Anti-de Sitter spaces, fluctuation modes remain stable for small negative mass-squared $m^2$. This follows from a real and positive total energy of the gravitational system. For finite cutoff $\epsilon$, we solve the Klein-Gordon equation numerically on regular hyperbolic tilings. When $\epsilon \to 0$, we find that the continuum BF bound is approached in a manner independent of the tiling. We confirm these results via simulations of a hyperbolic electric circuit. Moreover, we propose a novel circuit including active elements that allows to further scan values of $m^2$ above the BF bound.

arXiv comment11 pages, 9 figures, improved discussion and analysis, corrected typos

References in corpus (26)

• Gauge Theory Correlators from Non-Critical String Theory
• The World as a Hologram
• Lectures on holographic methods for condensed matter physics
• AdS/CFT Correspondence and Symmetry Breaking
• Topolectrical circuits
• Nonperturbative Quantum Gravity
• Quantum Gravity from Causal Dynamical Triangulations: A Review
• Conformality Lost
• Hyperbolic Lattices in Circuit Quantum Electrodynamics
• Simulating hyperbolic space on a circuit board
• Topolectric circuits: Theory and construction
• Crystallography of Hyperbolic Lattices
• Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry
• Topological hyperbolic lattices
• Active topolectrical circuits
• Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics
• Topological circuits of inductors and capacitors
• Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models
• Edge length dynamics on graphs with applications to $p$-adic AdS/CFT
• Holography on tessellations of hyperbolic space
• Lattice Setup for Quantum Field Theory in AdS${}_2$
• Modular discretization of the AdS2/CFT1 Holography
• Holography for Ising spins on the hyperbolic plane
• Hyperbolic Lattice for Scalar Field Theory in AdS${}_3$
• Holographic tensor networks from hyperbolic buildings
• The arithmetic geometry of AdS${}_2$ and its continuum limit

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