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.
Description
Phys. Rev. Lett. 130, 091604 (2023) - Breitenlohner-Freedman Bound on Hyperbolic Tilings
%0 Journal Article
%1 PhysRevLett.130.091604
%A Basteiro, Pablo
%A Dusel, Felix
%A Erdmenger, Johanna
%A Herdt, Dietmar
%A Hinrichsen, Haye
%A Meyer, René
%A Schrauth, Manuel
%D 2023
%I American Physical Society
%J Phys. Rev. Lett.
%K a
%N 9
%P 091604
%R 10.1103/PhysRevLett.130.091604
%T Breitenlohner-Freedman bound on hyperbolic tilings
%U https://link.aps.org/doi/10.1103/PhysRevLett.130.091604
%V 130
%X 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.
@article{PhysRevLett.130.091604,
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 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.},
added-at = {2023-10-23T12:51:00.000+0200},
author = {Basteiro, Pablo and Dusel, Felix and Erdmenger, Johanna and Herdt, Dietmar and Hinrichsen, Haye and Meyer, René and Schrauth, Manuel},
biburl = {https://www.bibsonomy.org/bibtex/28463178c4f5dac39e9ad721c39a3620f/ctqmat},
day = 02,
description = {Phys. Rev. Lett. 130, 091604 (2023) - Breitenlohner-Freedman Bound on Hyperbolic Tilings},
doi = {10.1103/PhysRevLett.130.091604},
interhash = {b143180e31c86dc960b8568751be2470},
intrahash = {8463178c4f5dac39e9ad721c39a3620f},
journal = {Phys. Rev. Lett.},
keywords = {a},
month = {03},
number = 9,
numpages = {7},
pages = 091604,
publisher = {American Physical Society},
timestamp = {2024-02-23T11:11:38.000+0100},
title = {Breitenlohner-Freedman bound on hyperbolic tilings},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.130.091604},
volume = 130,
year = 2023
}