Stress-Energy Tensor Induced by Bulk Dirac Spinor in Randall-Sundrum
  Model
  Motivated by the possible extension into a supersymmetric Randall-Sundrum
(RS) model, we investigate the properties of the vacuum expectation value (VEV)
of the stress-energy tensor for a quantized bulk Dirac spinor field in the RS
geometry and compare it with that for a real scalar field. This is carried out
via the Green function method based on first principles without invoking the
degeneracy factor, whose validity in a warp geometry is a priori unassured. In
addition, we investigate the local behavior of the Casimir energy near the two
branes. One salient feature we found is that the surface divergences near the
two branes have opposite signs. We argue that this is a generic feature of the
fermionic Casimir energy density due to its parity transformation in the fifth
dimension. Furthermore, we investigate the self-consistency of the RS metric
under the quantum correction due to the stress-energy tensor. It is shown that
the VEV of the stress-energy tensor and the classical one become comparable
near the visible brane if k ~ M ~ M_Pl (the requirement of no hierarchy
problem), where k is the curvature of the RS warped geometry and M the
5-dimensional Planck mass. In that case the self-consistency of RS model that
includes bulk fields is in doubt. If, however, k <~ M, then an approximate
self-consistency of the RS-type metric may still be satisfied.
