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We reveal elegant relations between the shape dependence of the Casimireffects and Weyl anomaly in boundary conformal field theories (BCFT). We showthat for any BCFT which has a description in terms of an effective action, thenear boundary divergent behavior of the renormalized stress tensor iscompletely determined by the central charges of the theory. These relations areverified by free BCFTs. We test them with holographic models of BCFT and findexact agreement. We propose that these relations between Casimir coefficientsand central charges hold for any BCFT. With the holographic models, wereproduce not only the precise form of the near boundary divergent behavior ofthe stress tensor, but also the surface counter term that is needed to make thetotal energy finite. As they are proportional to the central charges, the nearboundary divergence of the stress tensor must be physical and cannot be droppedby further artificial renormalization.Our results thus provide affirmativesupport on the physical nature of the divergent energy density near theboundary, whose reality has been a long-standing controversy in the literature.

Universality for Shape Dependence of Casimir Effects from Weyl Anomaly