Holographic Casimir Effect for Mixed Boundary Conditions and non-CFTs
This paper investigates the holographic Casimir effect in AdS/BCFT with a brane-localized scalar field. The scalar field takes different values at the strip's two boundaries, leading to mixed boundary conditions. The massive brane-localized scalar field typically breaks the boundary conformal symmetries, allowing us to study the holographic Casimir effect in non-CFTs. In two-dimensional spacetime, we apply the holographic g-theorem to prove the holographic bound on the Casimir effect for general brane-localized matter fields. In higher dimensions, we find that the brane-localized scalar field reduces the Casimir amplitude when the mass squared \(m^2=0\), but can increase it when \(m^2 < 0\). Additionally, there is a no-hair theorem for the cases where \(m^2>0\). These findings indicate that relevant boundary deformations can enhance the Casimir effect. As a byproduct, we obtain a gravitational dual of the repulsive Casimir force under mixed boundary conditions and argue that it aligns with the cosmic censorship conjecture.