Аннотация
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 m2. This follows from a real and positive total energy of the gravitational system. For finite cutoff ϵ, we solve the Klein-Gordon equation numerically on regular hyperbolic tilings. When ϵ→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 us to further scan values of m2 above the BF bound.
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