  The effective low energy description of interacting Dirac and Weyl semimetals
is that of massless quantum electrodynamics with several Lorentz breaking
material parameters. We perform a renormalization group analysis of Coulomb
interaction in anisotropic Dirac and Weyl semimetals and show that the
anisotropy persists in the material systems at the infrared fixed point. In
addition, a tilt of the fermion cones breaking inversion symmetry induces a
magnetoelectric term in the electrodynamics of the material whose magnitude
runs to match that of the electronic tilt at the fixed point.
