### abstract

- 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 details of the stabilization of the extra dimensions. In rugby ball solutions, 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. This allows the calculation of the shape of the low-energy pGB potential and response of the extra dimensional geometry as a function of the perturbing brane properties. If the pGB-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 the pGB. 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. We calculate the mass of the would-be zero mode, and 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.