Probing extra dimensions using Nambu-Goldstone bosons

TL;DR

This paper explores how Nambu-Goldstone bosons arising from brane fluctuations in higher-dimensional spacetime can be used to probe extra dimensions, deriving their effective action and constraining brane tension through supernova cooling.

Contribution

It provides an explicit form of the effective action for Nambu-Goldstone bosons on a brane and establishes bounds on brane tension from astrophysical observations.

Findings

Effective action for Nambu-Goldstone bosons derived

Couplings suppressed by brane fluctuation effects

String scale constrained by supernova cooling

Abstract

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. As was pointed out in the previous paper, the Kaluza-Klein mode couplings are suppressed by the effect of the brane fluctuation and the suppression is stronger if the brane tension is smaller. 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 of the supernova.