Bulk axions, brane back-reaction and fluxes

Extra-dimensional models can involve bulk pseudo-Goldstone bosons (pGBs) whose shift symmetry is explicitly broken only by physics localized on branes. Reliable calculation of their low-energy potential is often difficult because it requires an understanding of the dynamics that stabilizes the geometry of the extra dimensions. Rugby ball solutions provide simple examples of extra-dimensional configurations for which two compact extra dimensions are stabilized in the presence of only positive-tension brane sources. The effects of brane back-reaction can be computed explicitly for these systems, allowing the calculation of the shape of the low-energy pGB potential, V4D(φ), as a function of the perturbing brane properties, as well as the response of both the extra dimensional and on-brane geometries to this stabilization. If the φ-dependence is a small part of the total brane tension a very general analysis is possible, permitting an exploration of how the system responds to frustration when the two branes disagree on what the proper scalar vacuum should be. We show how the low-energy potential is given by the sum of brane tensions (in agreement with common lore) when only the brane tensions couple to φ. We also show how a direct brane coupling to the flux stabilizing the extra dimensions corrects this result in a way that does not simply amount to the contribution of the flux to the brane tensions. The mass of the low-energy pseudo-Goldstone mode is of order ma ∼ (μ/F)2mKK (where μ is the energy scale associated with the brane symmetry breaking and F < Mp is the extra-dimensional axion decay constant). In principle this can be larger or smaller than the Kaluza-Klein scale, mKK, but when it is larger axion properties cannot be computed purely within a 4D approximation (as they usually are). We briefly describe several potential applications, including a brane realization of ‘natural inflation,’ and a dynamical mechanism for suppressing the couplings of the pGB to matter localized on the branes. Since the scalar can be light enough to be relevant to precision tests of gravity (in a technically natural way) this mechanism can be relevant to evading phenomenological bounds.