A Note About Localized Photons on the Brane

The Maxwell action on the brane is obtained through a RandallSundrum dimentional reduction. Also, the self dual and the topologically massive actions for vectors in three dimensions can be obtained from Randall-Sundrum dimentional reduction. In the Randall-Sundrum mechanism[1], gravitons and scalar fields in D = d + 1 dimensions described by the Einstein-Hilbert and Klein-Gordon actions respectively, lead to gravitons and scalar fields localized on a ddimensional brane. But, the usual (second order) Maxwell action can not yield photons trapped on the brane[2]. A solution of this dilemma was achieved in ref.[3] where the photons localized on the brane in four dimensions come from two antisymmetric tensors in five dimensions, satisfying a self-dual action[4]. Specifically, Lu and Pope[3] found that the bosonic sector of ungauged N = 2, D = 4 supergravity can be obtained from N = 4, D = 5 gauged supergravity. The supersymmetric extension was considered by Duff, et al.[5] . The generalization for higher antisymmetric fields (p-forms) gives some negative results. Indeed, if we consider the Randall-Sundrum ansatz for the metric ds = egmn(x)dx dx + dz, (1) where m,n = 0, 1, ..., d, together with the natural anzatz for a p-form AM1...Mp(x,z) = AM1...Mp(x), (2)