## Abstract

We derive a general formalism for constructing a four-dimensional effective action for the radion field in 5 dimensions, taking into account the possible dependence of the scale factor on the internal coordinate. First and second variations of the action with respect to the size of the extra dimension reveals two types of algebraic constraints on the combination of brane and bulk Lagrangians that extremize the action, and provide an effective mass for the radion field. We derive a compact formula for the radion mass squared in terms of brane and bulk potentials for the case of a bulk scalar field. We further specialize these constraints for several, five-dimensional realizations of brane world models.

Original language | English (US) |
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Pages (from-to) | 146-158 |

Number of pages | 13 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 538 |

Issue number | 1-2 |

DOIs | |

State | Published - Jun 27 2002 |

### Bibliographical note

Funding Information:P.K. and K.A.O. would like to thank Ian I. Kogan and Antonios Papazoglou for helpful discussions at early stages of this work. M.P. would like to acknowledge the support of PPARC. The work of K.A.O. was supported partly by DOE grant DE-FG02-94ER-40823.