Localization and mass spectrum of q-form fields on branes

In this paper, we investigate localization of a bulk massless q-form field on codimension-one branes by using a new Kaluza–Klein (KK) decomposition, for which there are two types of KK modes for the bulk q-form field, the q  -form and (q−1)(q−1)-form modes. The first modes may be massive or massless while the second ones are all massless. These two types of KK modes satisfy two Schrödinger-like equations. For a five-dimensional brane model with a finite extra dimension, the spectrum of a bulk 3-form field on the brane consists of some massive bound 3-form KK modes as well as some massless bound 2-form ones with different configuration along the extra dimension. These 2-form modes are different from those obtained from a bulk 2-form field. For a five-dimensional degenerated Bloch brane model with an infinite extra dimension, some massive 3-form resonant KK modes and corresponding massless 2-form resonant ones are obtained for a bulk 3-form field.