# Conformal invariance of Electromagnetic field action

What is the significance of Conformal invariance of Electromagnetic field action? What does it lead to? And how can we break it?

Maxwell action is conformally invariant basically because of masslessness of photon, which implies that the action doesn't contain any dimensionful parameters. Such parameters would set the scale, and thus break the scaling symmetry. There is no proof that in $4D$ the scale invariance implies full conformal symmetry, but there are no counterexamples known. So the easiest way to break the conformal symmetry is to add the mass term to the Lagrangian $-m^2 A^{\mu} A_{\mu}$.