Often when talking about fixed points of the renormalization group that have certain nice properties like unitarity and Poincare invariance, we simply assume that the theory is conformal. As I will explain, this has never been proven in general. However, I will argue that unitarity and R-symmetry are enough to show that some classes of four dimensional fixed points are necessarily superconformal. In particular, I will argue that the conformal window of SQCD, which is widely assumed to be conformal, is indeed conformal.
