Constraints on branes' geometry from massive vector KK modes

Abstract: We examine the gauge invariance of massive vector Kaluza-Klein (KK) modes within various 6D brane models. Our analysis reveals that additional constraints on the brane's geometry are essential to maintain the gauge invariance of the massive vector KK modes. However, these conditions are not universally satisfied by brane solutions, leading to loss of gauge invariance. In instances where the brane solutions align with the conditions, we compute the mass spectra of both vector and scalar KK modes, and find some resonances for the KK modes in one of the brane models. Our findings indicate that the presence of a single type of massive scalar KK mode will break the gauge invariance.