IR free or interacting? A proposed diagnostic

We present and discuss a conjectured criterion for determining whether a 4d quantum field theory is IR free, or flows to an interacting conformal field theory in the infrared: 'the correct infrared phase is that with the larger conformal anomaly a'. A stronger conjecture is that 'an operator can become IR free only if that results in a larger conformal anomaly a'. We test these conjectures in the context of N=1 supersymmetric theories. They are verified to indeed predict the correct IR phase in every tested case, for a plethora of examples for which the infrared phase could already be determined on other grounds. When applied to the still unsettled case of SU(2) with a chiral superfield in the isospin 3/2 representation, the conjecture suggest that the IR phase is conformal rather than confining