Casimir Force of Fermions Coupled to Monopoles in Six Dimensional Spacetime

TL;DR

This paper computes the Casimir force for fermions in a six-dimensional spacetime with extra dimensions, revealing how topology and defect coupling influence the force's sign and magnitude.

Contribution

It introduces a detailed calculation of Casimir forces for fermions in higher-dimensional spaces with various topologies and defect couplings, highlighting the impact of extra-dimensional geometry.

Findings

Casimir force varies with extra-dimensional topology and defect coupling.

Opposite force signs observed for toroidal and spherical extra dimensions.

Results suggest topology and defects significantly influence quantum vacuum forces.

Abstract

We calculate the Casimir force for a fermionic quantum field in a piston geometry with three parallel plates. The fermion satisfies bag boundary conditions on the plates and the spacetime is assumed to have compact extra dimensions. The calculation is performed in the cases where the extra space has toroidal and spherical topology. We are mainly interested in the case in which the fermion is coupled non-trivially to an extra dimensional defect, with a torus extra dimensional topological background. We found that in certain limits, the Casimir force corresponding to the defect-fermion system and to the sphere, has opposite sign, in reference to those corresponding to the toroidal extra dimensional spaces.