%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 }