Holographic Bound of Casimir Effect in General Dimensions (2501.09886v2)

Abstract: Recently, it has been proposed that holography imposes a universal lower bound on the Casimir effect for 3d BCFTs. This paper generalizes the discussions to higher dimensions. We find Einstein gravity, DGP gravity, and Gauss-Bonnet gravity sets a universal lower bound of the strip Casimir effect in general dimensions. We verify the holographic bound by free theories and $O(N)$ models in the $\epsilon$ expansions. We also derive the holographic bound of the Casimir effect for a wedge and confirm free theories obey it. It implies holography sets a lower bound of the Casimir effect for general boundary shapes, not limited to the strip. Finally, we briefly comment on the impact of mass and various generalizations and applications of our results.

• The paper establishes a universal holographic lower bound on Casimir energy across various gravitational models.
• It employs rigorous analytical derivations and numerical simulations using strip and wedge geometries.
• The findings offer crucial insights into quantum vacuum fluctuations with implications for nanotechnology and cosmology.

Insights into the Holographic Bound of the Casimir Effect in General Dimensions

The investigation of the Casimir effect within the framework of holographic principles presents a significant intersection between quantum field theory, gravitation, and condensed matter physics. The paper "Holographic Bound of Casimir Effect in General Dimensions" by Rong-Xin Miao offers an in-depth exploration of this interplay, extending the understanding of Casimir effects beyond the conventional three-dimensional boundary conformal field theories (BCFTs) to general dimensions.

The central thesis of the paper is the proposal that holography—specifically under theories influenced by Einstein, Dvali-Gabadadze-Porrati (DGP), and Gauss-Bonnet (GB) gravitational theories—imposes a universal lower bound on the Casimir effect across different dimensions and boundary conditions. The Casimir effect, which originates from quantum vacuum fluctuations, manifests as an observable force between conducting plates. This effect has garnered significant interest due to its implications within nanotechnology and theoretical physics scenarios such as quantum chromodynamics and cosmology.

Holographic Ansatz and Derivation

The core derivation revolves around establishing a universal lower bound on the Casimir energy in diverse dimensional settings, leveraging holographic principles that often cite AdS/CFT correspondences. By employing various gravity models, the paper elucidates how these bounds are framed by constraints on the displacement operator norm—emerging from the breakdown of translational symmetry due to boundaries.

The author illustrates these considerations through comprehensive calculations using a strip geometry, which yields specific Casimir amplitudes contingent on boundary conditions. These are connected to the displacement operator through ratios that are conjectured to have a universal lower boundary limit.

Analytical and Numerical Insights

The paper presents detailed analytical derivations underscoring these bounds. Notably, for Einstein gravity, the minimal boundary tension scenario ($\rho \to -\infty$) yields ratios approaching universality. Furthermore, models incorporating higher derivative theories—such as GB gravity—demonstrate this bound's robustness. In DGP gravity's normal phase, analogous behavior is exhibited, consolidating the bound's applicability to a broad class of gravitational theories.

Numerical simulations supplement analytical results, especially concerning wedge geometries. The wedge—a generalization involving angled rather than parallel boundaries—presents intriguing divergence behaviors and is an area where theoretical expectations are tested against free BCFT cases to affirm the universality of the bounds.

Implications and Future Research Directions

The paper's findings have crucial implications: they suggest a fundamental limit on the size of the Casimir effect that can be physically realized, governed by holographic parameters. This insight can inform theoretical models involving BCFTs on more intricate geometrical constructs and contribute to the advancement of a deeper understanding of quantum gravitational dynamics.

Beyond theoretical extrapolations, practical implications may materialize in future nano-structured devices where the manipulation of quantum forces is crucial. Moreover, the results encourage further exploration of holographic principles in unconventional regimes, such as non-BCFT configurations, potentially broadening the scope of holography in capturing non-perturbative quantum effects.

In conclusion, the research thoroughly builds upon the interplay between holographic duality and quantum field theory, unveiling universal aspects of the Casimir effect transcending specific physical settings. The work paves an expansive path for theoretical advancements and presents a rich foundation for ensuing explorations into holography’s role in bounding quantum mechanical phenomena.