  We discuss the ultraviolet sector of 3+1 dimensional Lifshitz-type
anisotropic higher derivative scalar, fermion and gauge field theories, with
anisotropy exponent z=3 and with explicit breaking of Lorentz symmetry. By
discarding from the action all momentum dependent vertex operators, which is
essential to avoid phenomenologically unacceptable deformations of the light
cone, we find that renormalizable scalar self-interaction and Yukawa-like
couplings are, in general, asymptotically free. However, the requirement of
cancelling momentum dependent vertex operators is incompatible with gauge
symmetry and, therefore, for this kind of theories, gauge symmetry as well as
Lorentz symmetry are recovered only as emergent properties below some energy
scale M, that must be constrained from experiments. The quantum corrections to
the scalar mass and their impact on the hierarchy problem are also analyzed.
