Trace anomaly and Casimir effect

The Casimir energy for scaler field of two parallel conductors in two-dimen sional domain wall background, with Dirichlet boundary conditions, is calcu lated by making use of general properties of renormalized stress-tenser. We show that vacuum expectation values of stress-tenser contain two terms whi ch come from the boundary conditions and the gravitational background. In t wo dimensions the minimal coupling reduces to the conformal coupling and st ress-tenser can be obtained by the local and nonlocal contributions of the anomalous trace. This work shows that there exists a subtle and deep connec tion between Casimir effect and trace anomaly in curved space-time.