On Scale and Conformal Invariance in Four Dimensions

Understand

We study the implications of scale invariance in four-dimensional quantum field theories.

• Imposing unitarity, we find that infinitely many matrix elements vanish in a suitable kinematical configuration.
• This vanishing is a nontrivial necessary condition for conformality.
• We provide an argument why this is expected to be a sufficient condition as well, thereby linking scale and conformal invariance in unitary theories.