Stress-Energy Tensor Induced by Bulk Dirac Spinor in Randall-Sundrum Model

TL;DR

This paper analyzes the vacuum expectation value of the stress-energy tensor for a bulk Dirac spinor in the Randall-Sundrum model, revealing surface divergences and implications for the model's self-consistency with quantum corrections.

Contribution

It provides a first-principles Green function calculation of the stress-energy tensor for fermions in RS geometry and examines the quantum backreaction on the metric.

Findings

Surface divergences near branes have opposite signs.

Quantum stress-energy can challenge RS self-consistency if parameters are at the Planck scale.

Approximate self-consistency is possible if the curvature scale is below the Planck scale.

Abstract

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.