Antisymmetric Tensor Fields in the Locally Localized Gravity Models

We study the localization property of antisymmetric tensor fields in the locally localized gravity models. It is shown that all the antisymmetric tensor fields, including the vector field, in a bulk space-time are trapped on an AdS brane by a gravitational interaction where the presence of the brane cosmological constant plays an important role as in the cases of the other bulk fields. The normalized zero-modes spread rather widely in extra space so small extra dimensions might be needed in order not to conflict with experiment. E-mail address: [email protected] There has been a great deal of excitement recently over an alternative compactification scenario of space-time, where our four dimensional world emerges as a topological defect, a 3-brane, in a higher dimensional space-time [1, 2]. (This model was generalized to the case of many branes in Ref. [3].) In such ’brane world’ models, it is sometimes supposed that all the familiar matter and gauge fields are constrained to live on the brane, whereas gravity is free to propagate in the whole space-time. However, this treatment is not democratic at all as long as we do not have any reasonable mechanism of confinement of the matter and gauge fields on the brane. Thus, we should take account of all the local fields as bulk fields in the ’brane world’ models. In particular, one crux in the original Randall-Sundrum model is then how to localize the bulk gauge fields on a brane by a gravitational interaction. It is well known that in the Randall-Sundrum model the photon and the Kalb-Ramond field cannot be localized on the brane [4, 5, 6]. Recently, in Refs. [7, 8] we have developed a new mechanism for the localization of the bulk fields on the brane in the locally localized gravity models [9, 10, 11, 12, 13]. In this mechanism, the presence of the brane cosmological constant plays a crucial role. The aim of this paper is to study the localization property of the bulk antisymmetric tensor fields in the locally localized gravity models in detail. In previous works [7, 8], the antisymmetric tensor fields were not considered explicitly. But if we regard the models at hand as coming from superstring theory a bunch of antisymmetric tensor fields are expected to emerge in the low energy field theory so it is of importance to give a full analysis for the bulk antisymmetric tensor fields. Indeed, D-branes, in which D3 brane is one of candidates as our world, carry the nontrivial charges of the R-R antisymmetric tensor fields [14]. Moreover, it is pointed out that a brane with the charge of an antisymmetric tensor field might be stable owing to the charge conservation law [15]. First, we shall start with a locally localized gravity model by Karch and Randall in five dimensions [10]. Unlike their paper, we shall make use of the formulation adopted in our previous paper [8] since not only the translation to the Karch-Randall formulation but also the generalization to higher dimensions are straightforward. The metric ansatz we take is of the form [8]: ds(5) = gMNdx dx = e−A(r)ĝμνdxμdxν + dr = e−A(z)(ĝμνdxμdxν + dz), (1) where M, N, ... denote five-dimensional space-time indices and μ, ν, ...four-dimensional brane ones. The metric over the brane ĝμν denotes the four-dimensional anti-de Sitter metric. Moreover, e−A(r), e−A(z) and the relation between the ’radial’ r-coordinates and the ’conformal’ z-coordinates are given by e−A(r) = cosh ωr, e−A(z) = 1 sin ωz ,