Probing extra dimensions using Nambu–Goldstone bosons Original Research Article

We investigate a possibility that our four-dimensional world is a brane-like object embedded in a higher-dimensional spacetime. In such a situation, the transverse coordinates of the brane become the Nambu–Goldstone bosons which appear as a result of spontaneous breaking of the translation symmetry. We determine the form of the effective action of the system, finding the explicit form of the vierbein induced on the brane in terms of the Nambu–Goldstone boson variables and the bulk vielbein. The Kaluza–Klein mode couplings are suppressed by the effect of the Nambu–Goldstone bosons and the suppression is stronger with a smaller value of the brane tension. However we here show that the brane tension cannot be arbitrarily small since the inverse of the brane tension gives the coupling constant of the Nambu–Goldstone bosons. A rather stringent bound is obtained for the brane tension and the fundamental (‘string’) scale from the consideration of the cooling process in supernovas.