Casimir Energy in (2 + 1)-Dimensional Field Theories

TL;DR

This paper investigates how boundary conditions affect the Casimir energy in (2+1)-dimensional scalar and gauge theories, revealing two decay regimes and emphasizing the importance of boundary conditions and subdominant corrections.

Contribution

It identifies two distinct asymptotic decay regimes of Casimir energy based on boundary conditions in (2+1)D theories, combining analytical and numerical methods.

Findings

Two decay regimes for Casimir energy depending on boundary conditions

Exponential decay observed for Dirichlet boundary conditions in SU(2) gauge theories

Subdominant corrections are significant in low-temperature numerical simulations

Abstract

We explore the dependence of vacuum energy on the boundary conditions for massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the simplest geometrical setup given by a two-dimensional space bounded by two homogeneous parallel wires in order to compare it with the non-perturbative behaviour of the Casimir energy for non-Abelian gauge theories in (2 + 1) dimensions. Our results show the existence of two types of boundary conditions which give rise to two different asymptotic exponential decay regimes of the Casimir energy at large distances. The two families are distinguished by the feature that the boundary conditions involve or not interrelations between the behaviour of the fields at the two boundaries. Non-perturbative numerical simulations and analytical arguments show such an exponential decay for Dirichlet boundary conditions of SU(2) gauge theories. The verification that this behaviour is modified for other types of boundary conditions requires further numerical work. Subdominant corrections in the low-temperature regime are very relevant for numerical simulations, and they are also analysed in this paper.