## Stress-energy tensor induced by a bulk Dirac spinor in the Randall-Sundrum model

## 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 five-dimensional Planck mass. In that case themore »

- Authors:

- National Taiwan Univ., Taipei (Taiwan)
- National Taiwan Univ., Taipei (Taiwan); SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1443191

- Report Number(s):
- SLAC-PUB-14876

Journal ID: ISSN 1550-7998; PRVDAQ

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review. D, Particles, Fields, Gravitation and Cosmology

- Additional Journal Information:
- Journal Volume: 81; Journal Issue: 8; Journal ID: ISSN 1550-7998

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Shao, Shu-Heng, Chen, Pisin, and Gu, Je-An. Stress-energy tensor induced by a bulk Dirac spinor in the Randall-Sundrum model. United States: N. p., 2010.
Web. doi:10.1103/PhysRevD.81.084036.
```

```
Shao, Shu-Heng, Chen, Pisin, & Gu, Je-An. Stress-energy tensor induced by a bulk Dirac spinor in the Randall-Sundrum model. United States. doi:10.1103/PhysRevD.81.084036.
```

```
Shao, Shu-Heng, Chen, Pisin, and Gu, Je-An. Mon .
"Stress-energy tensor induced by a bulk Dirac spinor in the Randall-Sundrum model". United States. doi:10.1103/PhysRevD.81.084036. https://www.osti.gov/servlets/purl/1443191.
```

```
@article{osti_1443191,
```

title = {Stress-energy tensor induced by a bulk Dirac spinor in the Randall-Sundrum model},

author = {Shao, Shu-Heng and Chen, Pisin and Gu, Je-An},

abstractNote = {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 five-dimensional Planck mass. In that case the self-consistency of the 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.},

doi = {10.1103/PhysRevD.81.084036},

journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},

number = 8,

volume = 81,

place = {United States},

year = {2010},

month = {4}

}

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