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.