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 foliation preserving 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 physical scale $M_*$ emerges as a consequence of spontaneous conformal symmetry breaking of vacuum solution. It is demonstrated 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, it is also observed that the motion along the extra dimension can be highly suppressed and the five-dimensional theory can be effectively reduced to four-dimensional spacetime.