  An anisotropic model describing gravity--vector gauge coupling at all energy
scales is presented. The starting point is the 4+1 dimensional non--projectable
Ho\v{r}ava--Lifshitz gravity theory subject to a geometrical restriction.
Renormalizability arguments require all possible interactions in the potential
up to terms with $z=4$ spatial derivatives on the geometrical tensor fields:
the Riemann and Weyl tensors. The latter being necessary on a 4+1 dimensional
formulation. The dimensional reduction to 3+1 dimensions give rise to a model
invariant under {foliation--preserving diffeomorphisms} (FDiff) and $U(1)$
symmetry groups. The reduced theory on the {kinetic conformal} (KC) point
($\lambda =1/3$), propagates the same spectrum of the Einstein--Maxwell theory.
Moreover, at low energies, on the IR point $\alpha=0$, $\beta=1$, its field
equations are exactly the Einstein--Maxwell ones in a particular gauge
condition. The Minkowski ground state is stable provided several restrictions
on the coupling parameters are satisfied, they are explicitly obtained. The
quantum propagators of the physical degrees of freedom are obtained and after
an analysis of the first and second class constraints the renormalizability by
power counting is proved, provided that the aforementioned restrictions on the
coupling parameters are satisfied.
