  Electron-electron interactions in a Weyl semimetal are rigorously
investigated in a lattice model by non perturbative methods. The absence of
quantum phase transitions is proved for interactions not too large and short
ranged. The anisotropic Dirac cones persist with angles (Fermi velocities)
renormalized by the interaction, and with generically shifted Fermi points. As
in graphene, the optical conductivity shows universality properties: it is
equal to the massless Dirac fermions one with renormalized velocities, up to
corrections which are subdominant in modulus.
