Massive U (1) gauge fields and their accompanying scalars in brane world

Abstract In brane-world scenarios, the effective action of a massless bulk gauge field preserves gauge invariance via couplings between massive vector Kaluza-Klein (KK) and scalar KK modes. In this study, we extend this framework by introducing the term into the massless bulk gauge action. This modification explicitly breaks full gauge redundancy while preserving residual gauge symmetry both in the bulk and on the brane. In this setup, scalar KK modes can acquire masses from the background geometry. We find that, on the five-dimensional brane, these scalar KK modes are lighter than the vector KK modes. On the six-dimensional brane, two types of scalar modes emerge, and mixed interactions between them give rise to oscillations among these scalar modes.