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arXiv · 2205.05081

Breitenlohner-Freedman bound on hyperbolic tilings

Pablo Basteiro·Felix Dusel·Johanna Erdmenger·Dietmar Herdt·Haye Hinrichsen·René Meyer·Manuel Schrauth
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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 $\varepsilon$, we solve the Klein-Gordon equation numerically on regular hyperbolic tilings. When $\varepsilon\to0$, 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.

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Pablo Basteiro, Felix Dusel, Johanna Erdmenger, Dietmar Herdt, Haye Hinrichsen, René Meyer, Manuel Schrauth. 2022-05-10. Breitenlohner-Freedman bound on hyperbolic tilings. https://doi.org/10.1103/physrevlett.130.091604

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