Casimir Energy and Brane Stability

TL;DR

This paper explores how Casimir energy from various bulk fields can stabilize branes in five-dimensional models, potentially addressing hierarchy and cosmological inflation issues.

Contribution

It introduces a zeta-function regularization approach to compute the one-loop effective potential, demonstrating that Casimir energies can produce a stable brane configuration with implications for cosmology.

Findings

Casimir energies of bulk fields create a potential minimum for brane stabilization.

A scalar field coupled to a Lorentz-violating vector can aid in fine-tuning stabilization.

Casimir energy may contribute to the cosmological inflation epoch.

Abstract

We investigate the role of Casimir energy as a mechanism for brane stability in five-dimensional models with the fifth dimension compactified on an S^1\Z_2 orbifold, which includes the Randall-Sundrum two brane model (RS1). We employ a zeta-function regularization technique utilizing the Schwinger proper time method and the Jacobi theta function identity to calculate the one-loop effective potential. We show that the combination of the Casimir energies of a scalar Higgs field, the three generations of Standard Model fermions and one additional massive non-SM scalar in the bulk produce a non-trivial minimum of the potential. In particular, we consider a scalar field with a coupling in the bulk to a Lorentz violating vector particle localized to the compactified dimension. Such a scalar may provide a natural means of the fine-tuning needed for stabilization of the brane spearation. Lastly, we briefly review the possibility that Casimir energy plays a role in generating the currently observed epoch of cosmological inflation by examining a simple five-dimensional anisotropic metric.