Trace anomaly and Casimir effect

TL;DR

This paper investigates the relationship between the Casimir effect and trace anomaly in curved spacetime by calculating the Casimir energy of a scalar field in a two-dimensional domain wall background, highlighting the role of the anomalous trace.

Contribution

It demonstrates the connection between the Casimir effect and trace anomaly in curved spacetime, providing explicit calculations in a two-dimensional setting.

Findings

Vacuum stress tensor contains boundary and gravitational contributions.

Trace anomaly influences the Casimir energy in curved backgrounds.

Minimal coupling reduces to conformal coupling in two dimensions.

Abstract

The Casimir energy for scalar field of two parallel conductor 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 relation between Casimir effect and trace anomaly in curved space time.