A Vanishingly Small Vector Mass from Anisotropy of Higher Dimensional Spacetime

Abstract

We consider five-dimensional massive vector-gravity theory which is based on the foliationpreserving diffeomorphism and anisotropic conformal invariance. It does not have an intrinsic scale, and the only relevant parameter is the anisotropic factor z which characterizes the degree of anisotropy between the four-dimensional spacetime and the extra dimension. We assume that the physical scale M_* emerges as a consequence of spontaneous conformal symmetry breaking of the vacuum solution. We demonstrate that a very small mass for the vector particle compared to M_* can be achieved with a relatively mild adjustment of the parameter z. At the same time, the motion along the extra dimension is observed to be highly suppressed and the five-dimensional theory can be effectively reduced to four-dimensional spacetime.