Bound of Casimir Effect by Holography

Inspired by the Kovtun-Son-Starinet bound, we propose that holography imposes a lower bound on the Casimir effect. For simplicity, we focus on the Casimir effect between parallel planes for three-dimensional conformal field theories and briefly comment on the generalizations to other boundary shapes and higher dimensions. Remarkably, the ghost-free holographic models impose a universal lower bound on the Casimir effect. We verify the holographic bound by free theories, the Ising model, and $O(N)$ models with $N=2,3$ at critical points and prove it for the two-dimensional case. Remarkably, a general class of quantum field theories without conformal symmetries also obeys the holographic bound.