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.

11 pages, 9 figures, improved discussion and analysis, corrected typos

References in corpus (9)

• Nonperturbative Quantum Gravity
• Simulating hyperbolic space on a circuit board
• Topolectric circuits: Theory and construction
• Crystallography of Hyperbolic Lattices
• Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models
• Holography on tessellations of hyperbolic space
• Holography for Ising spins on the hyperbolic plane
• Hyperbolic Lattice for Scalar Field Theory in AdS${}_3$
• Holographic tensor networks from hyperbolic buildings

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