On Effective Theory of Brane World with Small Tension

The five dimensional theory compactified on $S^1$ with two ``branes'' (two domain walls) embedded in it is constructed, based on the field-theoretic mechanism to generate the ``brane''. Some light states localized in the ``brane'' appear in the theory. One is the Nambu-Goldstone boson, which corresponds to the breaking of the translational invariance in the transverse direction of the ``brane''. In addition, if the tension of the ``brane'' is smaller than the fundamental scale of the original theory, it is found that there may exist not only massless states but also some massive states lighter than the fundamental scale in the ``brane''. We analyze the four dimensional effective theory by integrating out the freedom of the fifth dimension. We show that some effective couplings can be explicitly calculated. As one of our results, some effective couplings of the state localized in the ``brane'' to the higher Kaluza-Klein modes in the bulk are found to be suppressed by the width of the ``brane''. The resultant suppression factor can be quantitatively different from the one analyzed by Bando et al. using the Nambu-Goto action, while they are qualitatively the same.