Ja n 20 01 Trace anomaly and Casimir effect

The Casimir energy for scalar field of two parallel conductors in two dimensional domain wall background, with Dirichlet boundary conditions, is calculated by making use of general properties of renormalized stress tensor. We show that vacuum expectation values of stress tensor contain two terms which come from the boundary conditions and the gravitational background. In two dimensions the minimal coupling reduces to the conformal coupling and stress tensor can be obtained by the local and non-local contribution of the anomalous trace. This work shows that there exists a subtle and deep connection between Casimir effect and trace anomaly in curved space time.