A Vanishingly Small Vector Mass from Anisotropy of Higher Dimensional Spacetime

TL;DR

This paper explores a five-dimensional vector-gravity model with anisotropic conformal invariance, demonstrating how a tiny vector mass can emerge naturally and how the extra dimension's effects can be suppressed, effectively reducing the theory to four dimensions.

Contribution

It introduces a novel five-dimensional massive vector-gravity framework with anisotropic conformal invariance, showing how a small vector mass and dimensional reduction can occur.

Findings

Achieves a very small vector mass relative to the scale $M_*$.

Shows suppression of motion along the extra dimension.

Demonstrates effective reduction to four-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.