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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>O</a:mi><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:math> models with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>N</e:mi><e:mo>=</e:mo><e:mn>2</e:mn></e:math>, 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.