Holographic Bound of Casimir Effect in General Dimensions

TL;DR

This paper extends the holographic lower bound on the Casimir effect from 3d BCFTs to higher dimensions, demonstrating its universality across various gravity theories and boundary geometries.

Contribution

It generalizes the holographic bound of the Casimir effect to higher dimensions and different boundary shapes, verified through free theories and $O(N)$ models.

Findings

Universal lower bound for the Casimir effect in higher dimensions.

Verification of the bound using free theories and $O(N)$ models.

Extension of the bound to wedge-shaped boundaries.

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.