# Casimir effect in rugby-ball type flux compactifications

## Abstract

As a continuation of the work by Minamitsuji, Naylor, and Sasaki [J. High Energy Phys. 12 (2006) 079], we discuss the Casimir effect for a massless bulk scalar field in a 4D toy model of a 6D warped flux compactification model, to stabilize the volume modulus. The one-loop effective potential for the volume modulus has a form similar to the Coleman-Weinberg potential. The stability of the volume modulus against quantum corrections is related to an appropriate heat kernel coefficient. However, to make any physical predictions after volume stabilization, knowledge of the derivative of the zeta function, {zeta}{sup '}(0) (in a conformally related spacetime) is also required. By adding up the exact mass spectrum using zeta-function regularization, we present a revised analysis of the effective potential. Finally, we discuss some physical implications, especially concerning the degree of the hierarchy between the fundamental energy scales on the branes. For a larger degree of warping our new results are very similar to the ones given by Minamitsuji, Naylor, and Sasaki [J. High Energy Phys. 12 (2006) 079] and imply a larger hierarchy. In the nonwarped (rugby ball) limit the ratio tends to converge to the same value, independently of the bulk dilaton coupling.

- Authors:

- Consejo Superior de Investigaciones Cientificas, ICE/CSIC and IEEC, Campus UAB, Fac Ciencies, 08193 Bellaterra (Barcelona) (Spain)
- ASC, Physics Department, LMU, Theresienstr. 37, Munich (Germany)
- (Japan)
- Department of Physics, Ritsumeikan University, Kusatsu, Shiga 525-8577 (Japan)

- Publication Date:

- OSTI Identifier:
- 21020178

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.064032; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BRANES; CASIMIR EFFECT; COMPACTIFICATION; CORRECTIONS; COSMOLOGY; COUPLING; MASS SPECTRA; POTENTIALS; QUANTUM FIELD THEORY; SCALAR FIELDS; SPACE-TIME; STABILIZATION; SUPERGRAVITY

### Citation Formats

```
Elizalde, Emilio, Minamitsuji, Masato, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, and Naylor, Wade.
```*Casimir effect in rugby-ball type flux compactifications*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.064032.

```
Elizalde, Emilio, Minamitsuji, Masato, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, & Naylor, Wade.
```*Casimir effect in rugby-ball type flux compactifications*. United States. doi:10.1103/PHYSREVD.75.064032.

```
Elizalde, Emilio, Minamitsuji, Masato, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, and Naylor, Wade. Thu .
"Casimir effect in rugby-ball type flux compactifications". United States.
doi:10.1103/PHYSREVD.75.064032.
```

```
@article{osti_21020178,
```

title = {Casimir effect in rugby-ball type flux compactifications},

author = {Elizalde, Emilio and Minamitsuji, Masato and Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 and Naylor, Wade},

abstractNote = {As a continuation of the work by Minamitsuji, Naylor, and Sasaki [J. High Energy Phys. 12 (2006) 079], we discuss the Casimir effect for a massless bulk scalar field in a 4D toy model of a 6D warped flux compactification model, to stabilize the volume modulus. The one-loop effective potential for the volume modulus has a form similar to the Coleman-Weinberg potential. The stability of the volume modulus against quantum corrections is related to an appropriate heat kernel coefficient. However, to make any physical predictions after volume stabilization, knowledge of the derivative of the zeta function, {zeta}{sup '}(0) (in a conformally related spacetime) is also required. By adding up the exact mass spectrum using zeta-function regularization, we present a revised analysis of the effective potential. Finally, we discuss some physical implications, especially concerning the degree of the hierarchy between the fundamental energy scales on the branes. For a larger degree of warping our new results are very similar to the ones given by Minamitsuji, Naylor, and Sasaki [J. High Energy Phys. 12 (2006) 079] and imply a larger hierarchy. In the nonwarped (rugby ball) limit the ratio tends to converge to the same value, independently of the bulk dilaton coupling.},

doi = {10.1103/PHYSREVD.75.064032},

journal = {Physical Review. D, Particles Fields},

number = 6,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}