Dual spaces of resonance in thick ρ-Branes

Full text: Antisymmetric tensor fields or simply differential forms arise naturally in string theory and supergravity and play an important role in dualization. In particular they appear in the R - R sector of each of the type II string theories. These tensor fields couple naturally to higher-dimensional extended objects, the D-branes and are important for their stability. Besides this, they are related to the linking number of higher dimensional knots. The rank of these antisymmetric tensors is defined by the dimension of the manifold. Beyond this, these kind of fields play an important role in the solution of the moduli stabilization problem of string theory. In this work we consider q-form fields in a ρ-brane embedded in a D = (ρ + 2) space-time. The membrane is generated by a domain wall in a Randall-Sundrum-like scenario. We study conditions for localization of zero modes of these fields. The expression agrees and generalizes the one found for the zero, one, two and three-forms in a 3-brane. By a generalization we mean that our expression is valid for any form in an arbitrary dimension with co dimension one. We also point out that, even without the dilaton coupling, some form fields are localized in the membrane. The massive modes are considered and the resonances are calculated using a numerical method. We find that different spaces have identical resonance structures, which we call dual spaces of resonances (DSR). (author)