Quantized bulk fermions in the Randall-Sundrum brane model

TL;DR

This paper computes quantum corrections from quantized massive fermions in the Randall-Sundrum model, analyzing boundary conditions, gauge invariance, and the potential for stabilizing extra dimensions, but finds hierarchy problem solutions require fine tuning.

Contribution

It extends previous scalar field analyses to include massive fermions, exploring their impact on radius stabilization and hierarchy problem in brane models.

Findings

Fermion quantum corrections can stabilize the extra dimension radius.

Hierarchy problem solutions require fine tuning of brane tensions.

Wilson loop symmetry breaking is analyzed in this context.

Abstract

The lowest order quantum corrections to the effective action arising from quantized massive fermion fields in the Randall-Sundrum background spacetime are computed. The boundary conditions and their relation with gauge invariance are examined in detail. The possibility of Wilson loop symmetry breaking in brane models is also analysed. The self-consistency requirements, previously considered in the case of a quantized bulk scalar field, are extended to include the contribution from massive fermions. It is shown that in this case it is possible to stabilize the radius of the extra dimensions but it is not possible to simultaneously solve the hierarchy problem, unless the brane tensions are dramatically fine tuned, supporting previous claims.