Electric-magnetic duality implies (global) conformal invariance

We have examined quantum theories of electric-magnetic duality-invariant vector fields enjoying classical conformal invariance in 4-dimensional flat spacetime. We extend Dirac’s argument about “the conditions for a quantum field theory to be relativistic” to “those for a quantum theory to be conformal”. We realize that electric-magnetic duality-invariant vector theories, together with classical conformal invariance defined in 4-d flat spacetime, are still conformally invariant theories when they are quantized in a way that electric magnetic-duality is manifest.