### Abstract

We consider the Casimir effect between two parallel plates localized on a brane. We argue that in order to properly compute the contribution to the Casimir energy due to any higher dimensional field, it is necessary to take into account the localization properties of the Kaluza-Klein modes. When the bulk field configuration is such that no massless mode appears in the spectrum, as, for instance, when the higher dimensional field obeys twisted boundary conditions across the branes, the correction to the Casimir energy is exponentially suppressed. When a massless mode is present in the spectrum, the correction to the Casimir energy can be, in principle, sizeable. However, when the bulk field is massless and strongly coupled to brane matter, the model is already excluded without resorting to any Casimir force experiment. The case which is in principle interesting is when the massless mode is not localized on the visible brane. We illustrate a method to compute the Casimir energy between two parallel plates, localized on the visible brane, approximating the Kaluza-Klein spectrum by truncation at the first excited mode. We treat this case by considering a pistonlike configuration and introduce a small parameter, ε, that takes into account the relative amplitude of the zero-mode wave function on the visible brane with respect to the massive excitation. We find that the Casimir energy is suppressed by two factors: at lowest order in ε, the correction to the Casimir energy comes entirely from the massive mode and turns out to be exponentially suppressed; the next-to-leading order correction in ε follows, instead, a power-law suppression due to the small wave-function overlap of the zero mode with matter confined on the visible brane. Generic comments on the constraints on new physics that may arise from Casimir force experiments are also made.

Original language | English |
---|---|

Article number | 124022 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 80 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2009 Dec 15 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*80*(12), [124022]. https://doi.org/10.1103/PhysRevD.80.124022

**Casimir effect on the brane.** / Flachi, Antonino; Tanaka, Takahiro.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 80, no. 12, 124022. https://doi.org/10.1103/PhysRevD.80.124022

}

TY - JOUR

T1 - Casimir effect on the brane

AU - Flachi, Antonino

AU - Tanaka, Takahiro

PY - 2009/12/15

Y1 - 2009/12/15

N2 - We consider the Casimir effect between two parallel plates localized on a brane. We argue that in order to properly compute the contribution to the Casimir energy due to any higher dimensional field, it is necessary to take into account the localization properties of the Kaluza-Klein modes. When the bulk field configuration is such that no massless mode appears in the spectrum, as, for instance, when the higher dimensional field obeys twisted boundary conditions across the branes, the correction to the Casimir energy is exponentially suppressed. When a massless mode is present in the spectrum, the correction to the Casimir energy can be, in principle, sizeable. However, when the bulk field is massless and strongly coupled to brane matter, the model is already excluded without resorting to any Casimir force experiment. The case which is in principle interesting is when the massless mode is not localized on the visible brane. We illustrate a method to compute the Casimir energy between two parallel plates, localized on the visible brane, approximating the Kaluza-Klein spectrum by truncation at the first excited mode. We treat this case by considering a pistonlike configuration and introduce a small parameter, ε, that takes into account the relative amplitude of the zero-mode wave function on the visible brane with respect to the massive excitation. We find that the Casimir energy is suppressed by two factors: at lowest order in ε, the correction to the Casimir energy comes entirely from the massive mode and turns out to be exponentially suppressed; the next-to-leading order correction in ε follows, instead, a power-law suppression due to the small wave-function overlap of the zero mode with matter confined on the visible brane. Generic comments on the constraints on new physics that may arise from Casimir force experiments are also made.

AB - We consider the Casimir effect between two parallel plates localized on a brane. We argue that in order to properly compute the contribution to the Casimir energy due to any higher dimensional field, it is necessary to take into account the localization properties of the Kaluza-Klein modes. When the bulk field configuration is such that no massless mode appears in the spectrum, as, for instance, when the higher dimensional field obeys twisted boundary conditions across the branes, the correction to the Casimir energy is exponentially suppressed. When a massless mode is present in the spectrum, the correction to the Casimir energy can be, in principle, sizeable. However, when the bulk field is massless and strongly coupled to brane matter, the model is already excluded without resorting to any Casimir force experiment. The case which is in principle interesting is when the massless mode is not localized on the visible brane. We illustrate a method to compute the Casimir energy between two parallel plates, localized on the visible brane, approximating the Kaluza-Klein spectrum by truncation at the first excited mode. We treat this case by considering a pistonlike configuration and introduce a small parameter, ε, that takes into account the relative amplitude of the zero-mode wave function on the visible brane with respect to the massive excitation. We find that the Casimir energy is suppressed by two factors: at lowest order in ε, the correction to the Casimir energy comes entirely from the massive mode and turns out to be exponentially suppressed; the next-to-leading order correction in ε follows, instead, a power-law suppression due to the small wave-function overlap of the zero mode with matter confined on the visible brane. Generic comments on the constraints on new physics that may arise from Casimir force experiments are also made.

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U2 - 10.1103/PhysRevD.80.124022

DO - 10.1103/PhysRevD.80.124022

M3 - Article

VL - 80

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 12

M1 - 124022

ER -